UNITED STATES
SECURITIES AND EXCHANGE COMMISSION
Washington, DC 20549

FORM N-Q

QUARTERLY SCHEDULE OF PORTFOLIO HOLDINGS OF REGISTERED MANAGEMENT INVESTMENT COMPANY

Investment Company Act file number         811-7606         

        Nuveen Connecticut Premium Income Municipal Fund         
(Exact name of registrant as specified in charter)

        333 West Wacker Drive, Chicago, Illinois, 60606         
Address of principal executive offices) (Zip code)

Jessica R. Droeger—Vice President and Secretary
        333 West Wacker Drive, Chicago, Illinois, 60606         
(Name and address of agent for service)

Registrant's telephone number, including area code:         312-917-7700        

Date of fiscal year end:            05/31          

Date of reporting period:          08/31/04         

Form N-Q is to be used by management investment companies, other than small business investment companies registered on Form N-5 (§§ 239.24 and 274.5 of this chapter), to file reports with the Commission, not later than 60 days after the close of the first and third fiscal quarters, pursuant to rule 30b1-5 under the Investment Company Act of 1940 (17 CFR 270.30b1-5). The Commission may use the information provided on Form N-Q in its regulatory, disclosure review, inspection, and policymaking roles.

A registrant is required to disclose the information specified by Form N-Q, and the Commission will make this information public. A registrant is not required to respond to the collection of information contained in Form N-Q unless the Form displays a currently valid Office of Management and Budget (“OMB”) control number. Please direct comments concerning the accuracy of the information collection burden estimate and any suggestions for reducing the burden to the Secretary, Securities and Exchange Commission, 450 Fifth Street, NW, Washington, DC 20549-0609. The OMB has reviewed this collection of information under the clearance requirements of 44 U.S.C. § 3507.

Item 1. Schedule of Investments

Portfolio of Investments (Unaudited)
Nuveen Connecticut Premium Income Municipal Fund (NTC)
August 31, 2004

	Principal		Optional Call		Market
	Amount (000)	Description(1)	Provisions*	Ratings**	Value
		Consumer Staples - 1.8%
$	1,625	Puerto Rico, The Children's Trust Fund, Tobacco Settlement Asset-Backed Refunding Bonds, Series	5/12 at 100.00	BBB	$    1,473,241
		2002, 5.375%, 5/15/33
		Education and Civic Organizations - 34.5%
		Connecticut Higher Education Supplemental Loan Authority, Revenue Bonds, Family Education Loan
		Program, Series 1996A:
	860	5.800%, 11/15/14 (Alternative Minimum Tax) - AMBAC Insured	11/06 at 102.00	AAA	861,978
	545	5.875%, 11/15/17 (Alternative Minimum Tax) - AMBAC Insured	11/06 at 102.00	AAA	546,270
	545	Connecticut Higher Education Supplemental Loan Authority, Revenue Bonds, Family Education Loan	11/09 at 102.00	AAA	564,451
		Program, Series 1999A, 6.000%, 11/15/18 (Alternative Minimum Tax) - AMBAC Insured
	900	Connecticut Higher Education Supplemental Loan Authority, Revenue Bonds, Family Education Loan	11/11 at 100.00	Aaa	947,025
		Program, Series 2001A, 5.250%, 11/15/18 (Alternative Minimum Tax) - MBIA Insured
	1,500	Connecticut Health and Educational Facilities Authority, Revenue Bonds, Loomis Chaffee School,	7/06 at 102.00	AAA	1,600,755
		Series 1996C, 5.500%, 7/01/16 - MBIA Insured
	1,900	Connecticut Health and Educational Facilities Authority, Revenue Bonds, Fairfield University,	7/08 at 102.00	AAA	1,972,637
		Series 1998H, 5.000%, 7/01/23 - MBIA Insured
	2,920	Connecticut Health and Educational Facilities Authority, Revenue Bonds, Connecticut College, Series	7/07 at 102.00	AAA	3,179,617
		1997C-1, 5.500%, 7/01/20 - MBIA Insured
	2,525	Connecticut Health and Educational Facilities Authority, Revenue Bonds, Connecticut State	11/12 at 100.00	AAA	2,761,315
		University System, Series 2003E, 5.000%, 11/01/15 - FGIC Insured
	1,250	Connecticut Health and Educational Facilities Authority, Revenue Bonds, Fairfield University,	7/09 at 101.00	AAA	1,321,187
		Series 1999I, 5.250%, 7/01/25 - MBIA Insured
	750	Connecticut Health and Educational Facilities Authority, Revenue Bonds, Horace Bushnell Memorial	7/09 at 101.00	Aaa	818,002
		Hall, Series 1999A, 5.625%, 7/01/29 - MBIA Insured
	500	Connecticut Health and Educational Facilities Authority, Revenue Bonds, Trinity College, Series	7/11 at 101.00	AAA	513,075
		2001G, 5.000%, 7/01/31 - AMBAC Insured
	650	Connecticut Health and Educational Facilities Authority, Revenue Bonds, Loomis Chaffee School,	7/11 at 101.00	A2	701,981
		Series 2001D, 5.500%, 7/01/23
	450	Connecticut Health and Educational Facilities Authority, Revenue Bonds, Greenwich Academy, Series	3/11 at 101.00	AAA	460,251
		2001B, 5.000%, 3/01/32 - FSA Insured
	2,000	Connecticut Health and Educational Facilities Authority, Revenue Bonds, University of Hartford,	7/12 at 101.00	AA	2,056,320
		Series 2002E, 5.250%, 7/01/32 - RAAI Insured
	1,500	Connecticut Health and Educational Facilities Authority, Revenue Bonds, Yale University, Series	7/09 at 100.00	AAA	1,537,350
		2002W, 5.125%, 7/01/27
	1,500	Connecticut Health and Educational Facilities Authority, Revenue Bonds, Yale University, Series	7/13 at 100.00	AAA	1,524,975
		2003X-1, 5.000%, 7/01/42
	925	Connecticut Health and Educational Facilities Authority, Revenue Bonds, Brunswick School, Series	7/13 at 100.00	AAA	948,514
		2003B, 5.000%, 7/01/33 - MBIA Insured
	1,000	University of Connecticut, Student Fee Revenue Refunding Bonds, Series 2002A, 5.250%, 11/15/19 -	11/12 at 101.00	AAA	1,101,620
		FGIC Insured
	1,100	University of Connecticut, General Obligation Bonds, Series 2003A, 5.125%, 2/15/21 - MBIA Insured	2/13 at 100.00	AAA	1,178,078
		University of Connecticut, General Obligation Bonds, Series 2004A:
	1,000	5.000%, 1/15/18 - MBIA Insured	1/14 at 100.00	AAA	1,086,850
	2,000	5.000%, 1/15/19 - MBIA Insured	1/14 at 100.00	AAA	2,160,640
		Healthcare - 11.1%
	2,000	Connecticut Health and Educational Facilities Authority, Revenue Bonds, Stamford Hospital, Series	7/09 at 101.00	Aaa	2,058,140
		1999G, 5.000%, 7/01/24 - MBIA Insured
	1,000	Connecticut Health and Educational Facilities Authority, Revenue Bonds, William W. Backus Hospital,	7/07 at 102.00	AAA	1,090,440
		Series 1997D, 5.750%, 7/01/27 - AMBAC Insured
	3,000	Connecticut Health and Educational Facilities Authority, Revenue Refunding Bonds, Middlesex Health	7/07 at 101.00	Aaa	3,058,650
		Services, Series 1997H, 5.125%, 7/01/27 - MBIA Insured
	2,000	Connecticut Health and Educational Facilities Authority, Revenue Bonds, Eastern Connecticut Health	7/10 at 101.00	AA	2,207,320
		Network, Series 2000A, 6.000%, 7/01/25 - RAAI Insured
	500	Connecticut Health and Educational Facilities Authority, Revenue Bonds, Bristol Hospital, Series	7/12 at 101.00	AA	541,710
		2002B, 5.500%, 7/01/21 - RAAI Insured
		Housing/Multifamily - 4.5%
	1,000	Connecticut Housing Finance Authority, Housing Mortgage Finance Program Bonds, Series 1999D-2,	12/09 at 100.00	AAA	1,045,850
		6.200%, 11/15/41 (Alternative Minimum Tax)
	605	Waterbury Nonprofit Housing Corporation, Connecticut, FHA-Insured Section 8 Mortgage Revenue Bonds,	1/05 at 100.00	AAA	606,724
		Fairmount Heights Project, Series 1993A, 6.500%, 7/01/07 - MBIA Insured
	1,885	Williamantic Housing Authority, Connecticut, GNMA Collateralized Mortgage Loan Multifamily Housing	10/05 at 105.00	AAA	2,012,860
		Revenue Bonds, Village Heights Apartments, Series 1995A, 8.000%, 10/20/30
		Housing/Single Family - 2.9%
	350	Connecticut Housing Finance Authority, Housing Mortgage Finance Program Bonds, Series 2001A-1,	5/10 at 100.00	AAA	358,806
		5.250%, 11/15/28
	25	Connecticut Housing Finance Authority, Housing Mortgage Finance Program Bonds, Series 2001A-2,	9/04 at 100.00	AAA	25,075
		5.450%, 5/15/32 (Alternative Minimum Tax) (Pre-refunded to 9/30/04)
	1,000	Connecticut Housing Finance Authority, Housing Mortgage Finance Program Bonds, Series 2001C,	11/10 at 100.00	AAA	1,018,370
		5.300%, 11/15/33 (Alternative Minimum Tax)
	945	Connecticut Housing Finance Authority, Housing Mortgage Finance Program Bonds, Series 2001D-2,	9/04 at 100.00	AAA	947,741
		5.350%, 11/15/32 (Alternative Minimum Tax) (Pre-refunded to 9/30/04)
		Long-Term Care - 7.3%
	1,300	Connecticut Health and Educational Facilities Authority, FHA-Insured Mortgage Revenue Bonds, Hebrew	8/08 at 102.00	AAA	1,328,340
		Home and Hospital, Series 1999B, 5.200%, 8/01/38
	750	Connecticut Development Authority, First Mortgage Gross Revenue Refunding Healthcare Bonds, Church	4/07 at 102.00	BBB-	758,625
		Homes Inc. - Congregational Avery Heights, Series 1997, 5.700%, 4/01/12
	615	Connecticut Development Authority, First Mortgage Gross Revenue Refunding Healthcare Bonds,	9/09 at 102.00	AA	671,980
		Connecticut Baptist Homes Inc., Series 1999, 5.500%, 9/01/15 - RAAI Insured
		Connecticut Development Authority, Revenue Refunding Bonds, Duncaster Inc., Series 1999A:
	1,000	5.250%, 8/01/19 - RAAI Insured	2/10 at 102.00	AA	1,056,890
	1,000	5.375%, 8/01/24 - RAAI Insured	2/10 at 102.00	AA	1,049,050
	1,000	Connecticut Development Authority, Health Facility Revenue Refunding Bonds, Alzheimer's Resource	2/05 at 102.00	N/R	1,005,730
		Center of Connecticut Inc., Series 1994A, 7.000%, 8/15/09
		Tax Obligation/General - 26.2%
	500	Bridgeport, Connecticut, General Obligation Bonds, Series 2004C, 5.250%, 8/15/14 - MBIA Insured	No Opt. Call	AAA	564,885
	750	Bridgeport, Connecticut, General Obligation Refunding Bonds, Series 2002A, 5.375%, 8/15/19 -	8/12 at 100.00	Aaa	830,595
		FGIC Insured
	1,000	Bridgeport, Connecticut, General Obligation Bonds, Series 2003A, 5.250%, 9/15/23 - FSA Insured	9/13 at 100.00	AAA	1,065,500
		Cheshire, Connecticut, General Obligation Bonds, Series 1999:
	660	5.625%, 10/15/16	10/09 at 101.00	Aa3	742,177
	660	5.625%, 10/15/17	10/09 at 101.00	Aa3	740,843
	2,000	Connecticut, General Obligation Bonds, Series 2002B, 5.500%, 6/15/21	6/12 at 100.00	AA	2,216,580
	1,500	Connecticut, General Obligation Bonds, Series 2002A, 5.375%, 4/15/19	4/12 at 100.00	AA	1,646,160
	1,110	Connecticut, General Obligation Bonds, Series 2004C, 5.000%, 4/01/23 - FGIC Insured	4/14 at 100.00	AAA	1,167,343
	1,000	Hartford, Connecticut, General Obligation Bonds, Series 2000, 5.500%, 6/15/20 - FGIC Insured	6/10 at 102.00	AAA	1,108,420
	400	Northern Mariana Islands, General Obligation Bonds, Series 2000A, 6.000%, 6/01/20 - ACA Insured	6/10 at 100.00	A	425,176
	1,500	Puerto Rico, Public Improvement General Obligation Refunding Bonds, Series 2001A, 5.500%,	No Opt. Call	AAA	1,755,195
		7/01/20 - MBIA Insured
		Regional School District 16, Beacon Falls and Prospect, Connecticut, General Obligation Bonds,
		Series 2000:
	350	5.500%, 3/15/18 - FSA Insured	3/10 at 101.00	Aaa	389,123
	350	5.625%, 3/15/19 - FSA Insured	3/10 at 101.00	Aaa	392,515
	350	5.700%, 3/15/20 - FSA Insured	3/10 at 101.00	Aaa	393,796
	1,420	Regional School District 16, Connecticut, General Obligation Bonds, Series 2003, 5.000%, 3/15/16 -	3/13 at 101.00	Aaa	1,563,917
		AMBAC Insured
	2,105	Stratford, Connecticut, General Obligation Bonds, Series 2002, 4.000%, 2/15/15 - FSA Insured	2/12 at 100.00	AAA	2,157,520
	1,000	Waterbury, Connecticut, General Obligation Bonds, Series 2002A, 5.375%, 4/01/17 - FSA Insured	4/12 at 100.00	AAA	1,114,250
	965	Waterbury, Connecticut, General Obligation Tax Revenue Intercept Bonds, Series 2000, 6.000%,	2/09 at 101.00	AA	1,062,677
		2/01/19 - RAAI Insured
	1,630	Westport, Connecticut, General Obligation Bonds, Series 2003, 4.750%, 2/01/19	2/12 at 100.00	Aaa	1,708,273
		Tax Obligation/Limited - 20.1%
	1,900	Capitol Region Education Council, Connecticut, Revenue Bonds, Series 1995, 6.700%, 10/15/10	10/05 at 102.00	BBB	1,990,117
	2,000	Connecticut Health and Educational Facilities Authority, Revenue Bonds, Child Care Facilities	7/09 at 102.00	AAA	2,181,400
		Program, Series 1999C, 5.625%, 7/01/29 - AMBAC Insured
	1,000	Connecticut, Special Tax Obligation Transportation Infrastructure Purpose Bonds, Series 2002A,	7/12 at 100.00	AAA	1,113,740
		5.375%, 7/01/19 - FSA Insured
		Connecticut, Special Tax Obligation Transportation Infrastructure Purpose Bonds, Series 2002B:
	2,000	5.000%, 12/01/20 - AMBAC Insured	12/12 at 100.00	AAA	2,133,880
	1,000	5.000%, 12/01/21 - AMBAC Insured	12/12 at 100.00	AAA	1,058,450
	500	Connecticut, Special Tax Obligation Transportation Infrastructure Purpose Bonds, Series 2003B,	1/14 at 100.00	AAA	525,270
		5.000%, 1/01/23 - FGIC Insured
	1,700	Connecticut, Special Tax Obligation Transportation Infrastructure Purpose Bonds, Series 1991B,	No Opt. Call	AA-	2,028,559
		6.500%, 10/01/10
	625	Connecticut, Special Obligation Rate Reduction Bonds, Series 2004A, 5.000%, 6/30/11	No Opt. Call	AAA	696,988
	2,000	Puerto Rico Municipal Finance Agency, Series 2002A, 5.250%, 8/01/21 - FSA Insured	8/12 at 100.00	AAA	2,184,020
	1,000	Virgin Islands Public Finance Authority, Gross Receipts Taxes Loan Notes, Series 1999A,	10/10 at 101.00	BBB	1,141,050
		6.500%, 10/01/24
	1,000	Virgin Islands Public Finance Authority, Gross Receipts Taxes Loan Notes, Series 2003, 5.250%,	10/14 at 100.00	AAA	1,111,190
		10/01/19 - FSA Insured
		Transportation - 2.2%
	750	Connecticut, General Airport Revenue Bonds, Bradley International Airport, Series 2001A, 5.125%,	4/11 at 101.00	AAA	762,210
		10/01/26 (Alternative Minimum Tax) - FGIC Insured
	1,000	Hartford, Connecticut, Parking System Revenue Bonds, Series 2000A, 6.400%, 7/01/20	7/10 at 100.00	Baa2	1,043,240
		U.S. Guaranteed*** - 12.4%
	1,500	Bridgeport, Connecticut, General Obligation Bonds, Series 2000A, 6.000%, 7/15/19 (Pre-refunded to	7/10 at 101.00	AAA	1,761,135
		7/15/10) - FGIC Insured
	1,060	Puerto Rico, The Children's Trust Fund, Tobacco Settlement Asset-Backed Bonds, Series 2000,	7/10 at 100.00	AAA	1,158,251
		5.750%, 7/01/20 (Pre-refunded to 7/01/10)
	40	Connecticut, General Obligation Bonds, Series 1993E, 6.000%, 3/15/12	No Opt. Call	AA***	47,211
	2,000	Connecticut Health and Educational Facilities Authority, Revenue Bonds, Trinity College, Series	7/06 at 102.00	AAA	2,189,000
		1996E, 5.875%, 7/01/26 (Pre-refunded to 7/01/06) - MBIA Insured
	1,000	Connecticut, Special Tax Obligation Transportation Infrastructure Purpose Bonds, Series 1999A,	12/09 at 101.00	AAA	1,148,330
		5.625%, 12/01/19 (Pre-refunded to 12/01/09) - FGIC Insured
	1,000	Connecticut, Special Assessment Revenue Bonds, Second Injury Fund, Series 2000A, 5.250%, 1/01/14	1/11 at 101.00	AAA	1,131,270
		(Pre-refunded to 1/01/11) - FSA Insured
	1,000	Connecticut, Clean Water Fund Revenue Bonds, Series 2001, 5.500%, 10/01/20 (Pre-refunded	10/11 at 100.00	AAA	1,149,150
		to 10/01/11)
	300	Puerto Rico, Public Improvement General Obligation Refunding Bonds, Series 2001, 5.125%, 7/01/30	7/11 at 100.00	AAA	337,827
		(Pre-refunded to 7/01/11) - FSA Insured
	1,000	Puerto Rico Infrastructure Financing Authority, Special Obligation Bonds, Series 2000A,	10/10 at 101.00	AAA	1,078,280
		5.500%, 10/01/40
		Utilities - 9.5%
	1,500	Connecticut Development Authority, Pollution Control Revenue Refunding Bonds, Connecticut Light and	10/08 at 102.00	A3	1,575,960
		Power Company, Series 1993A, 5.850%, 9/01/28
	2,255	Connecticut Resource Recovery Authority, Revenue Bonds, American Ref-Fuel Company of Southeastern	11/04 at 100.00	AAA	2,277,911
		Connecticut, Series 1989A, 7.700%, 11/15/11 - MBIA Insured
	1,750	Connecticut Resource Recovery Authority, Corporate Credit Revenue Bonds, American Ref-Fuel Company	12/11 at 102.00	Baa2	1,815,993
		of Southeastern Connecticut, Series 2001A-I, 5.500%, 11/15/15 (Alternative Minimum Tax)
		Eastern Connecticut Resource Recovery Authority, Solid Waste Revenue Bonds, Wheelabrator Lisbon
		Project, Series 1993A:
	395	5.500%, 1/01/14 (Alternative Minimum Tax)	1/05 at 100.00	BBB	396,114
	1,590	5.500%, 1/01/20 (Alternative Minimum Tax)	1/05 at 100.00	BBB	1,589,889
		Water and Sewer - 13.4%
	1,185	Connecticut, State Revolving Fund General Revenue Bonds, Series 2003A, 5.000%, 10/01/16	10/13 at 100.00	AAA	1,299,530
	1,500	Connecticut, State Revolving Fund General Revenue Bonds, Series 2003B, 5.000%, 10/01/12	No Opt. Call	AAA	1,680,720
	1,400	Connecticut Development Authority, Water Facilities Revenue Refunding Bonds, Bridgeport Hydraulic	12/04 at 101.00	AAA	1,417,444
		Company, Series 1993B, 5.500%, 6/01/28 - MBIA Insured
	2,550	Connecticut Development Authority, Water Facilities Revenue Bonds, Bridgeport Hydraulic Company,	9/06 at 102.00	AAA	2,758,233
		Series 1996, 6.000%, 9/01/36 (Alternative Minimum Tax) - AMBAC Insured
		South Central Connecticut Regional Water Authority, Water System Revenue Bonds, Eighteenth
		Series 2003A:
	1,000	5.000%, 8/01/20 - MBIA Insured	8/13 at 100.00	AAA	1,070,860
	1,525	5.000%, 8/01/33 - MBIA Insured	8/13 at 100.00	AAA	1,567,452
	1,000	Stamford, Connecticut, Water Pollution Control System and Facility Revenue Bonds, Series 2003A,	11/13 at 100.00	AA+	1,020,340
		5.000%, 11/15/32
$	110,195	Total Long-Term Investments (cost $111,698,936) - 145.9%			117,644,392
		Other Assets Less Liabilities - 1.6%			1,269,103
		Preferred Shares, at Liquidation Value - (47.5)%			(38,300,000)
		Net Assets Applicable to Common Shares - 100%			$80,613,495

(1)	All percentages shown in the Portfolio of Investments are based on net assets applicable to Common
	shares.
*	Optional Call Provisions: Dates (month and year) and prices of the earliest optional call or redemption.
	There may be other call provisions at varying prices at later dates.
**	Ratings: Using the higher of Standard & Poor's or Moody's rating.
***	Securities are backed by an escrow or trust containing sufficient U.S. Government or U.S. Government
	agency securities which ensures the timely payment of principal and interest. Such securities are
	normally considered to be equivalent to AAA rated securities.
N/R	Investment is not rated.
	Income Tax Information
	The following information is presented on an income tax basis. Differences between amounts for financial
	statement and federal income tax purposes are primarily due to timing differences in recognizing income
	on taxable market discount securities and timing differences in recognizing certain gains and losses on
	security transactions.
	At August 31, 2004, the cost of investments was $111,686,127.
	Gross unrealized appreciation and gross unrealized depreciation of investments at August 31, 2004,
	were as follows:
	Gross unrealized:
	Appreciation	$6,156,847
	Depreciation	(198,582)
	Net unrealized appreciation of investments	$5,958,265

Item 2. Controls and Procedures.

1. The registrant's principal executive and principal financial officers, or persons performing similar functions, have concluded that the registrant's disclosure controls and procedures (as defined in Rule 30a-3(c) under the Investment Company Act of 1940, as amended (the "1940 Act") (17 CFR 270.30a-3(c))) are effective, as of a date within 90 days of the filing date of this report that includes the disclosure required by this paragraph, based on their evaluation of the controls and procedures required by Rule 30a-3(b) under the 1940 Act (17 CFR 270.30a-3(b)) and Rule 13a-15(b) or 15d-15(b) under the Securities Exchange Act of 1934, (17 CFR 240.13a-15(b) or 240.15d-15(b)).
2. There were no changes in the registrant's internal control over financial reporting (as defined in Rule 30a-3(d) under the 1940 Act (17 CFR 270.30a-3(d)) that occurred during the registrant's last fiscal quarter that has materially affected, or is reasonably likely to materially affect, the registrant's internal control over financial reporting.

Item 3. Exhibits.

File as exhibits as part of this Form a separate certification for each principal executive officer and principal financial officer of the registrant as required by Rule 30a-2(a) under the Act (17 CFR 270.30a-2(a)), exactly as set forth below: EX-99 CERT Attached hereto.

SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934 and the Investment Company Act of 1940, the registrant has duly caused this report to be signed on its behalf by the undersigned, thereunto duly authorized.

(Registrant)         Nuveen Connecticut Premium Income Municipal Fund        

By (Signature and Title)*          /s/ Jessica R. Droeger--Vice President and Secretary        

Date         10/29/04        

Pursuant to the requirements of the Securities Exchange Act of 1934 and the Investment Company Act of 1940, this report has been signed below by the following persons on behalf of the registrant and in the capacities and on the dates indicated.

By (Signature and Title)*         /s/ Gifford R. Zimmerman--Chief Administrative Officer (Principal Executive Officer)        

Date         10/29/04        

By (Signature and Title)*         /s/ Stephen D. Foy--Vice President and Controller (Principal Financial Officer)        

Date         10/29/04        

* Print the name and title of each signing officer under his or her signature.