<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0303</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2011-01-05</periodOfReport>

    <issuer>
        <issuerCik>0000899752</issuerCik>
        <issuerName>NUVEEN CONNECTICUT PREMIUM INCOME MUNICIPAL FUND</issuerName>
        <issuerTradingSymbol>NTC</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000070858</rptOwnerCik>
            <rptOwnerName>BANK OF AMERICA CORP /DE/</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>BANK OF AMERICA CORPORATE CENTER</rptOwnerStreet1>
            <rptOwnerStreet2>100 N. TRYON STREET</rptOwnerStreet2>
            <rptOwnerCity>CHARLOTTE</rptOwnerCity>
            <rptOwnerState>NC</rptOwnerState>
            <rptOwnerZipCode>28255</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001102113</rptOwnerCik>
            <rptOwnerName>BANK OF AMERICA NA</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>BANK OF AMERICA CORPORATE CENTER</rptOwnerStreet1>
            <rptOwnerStreet2>100 NORTH TRYON STREET</rptOwnerStreet2>
            <rptOwnerCity>CHARLOTTE</rptOwnerCity>
            <rptOwnerState>NC</rptOwnerState>
            <rptOwnerZipCode>28255</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000728612</rptOwnerCik>
            <rptOwnerName>MERRILL LYNCH, PIERCE, FENNER &amp; SMITH INC.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>4 WORLD FINANCIAL CENTER NORTH TOWER</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10080</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Auction Rate Preferred</value>
                <footnoteId id="F1"/>
            </securityTitle>
            <transactionDate>
                <value>2011-01-05</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F2"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>113</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F1"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The Auction Rate Preferred Shares (&quot;Shares&quot;) reported in Table I represent Shares beneficially owned by Bank of America, N.A. (&quot;BANA&quot;), Merrill Lynch, Pierce, Fenner &amp; Smith, Inc. (&quot;MLPFS&quot;), both of which are wholly owned subsidiaries of Bank of America Corporation (&quot;Bank of America&quot;).</footnote>
        <footnote id="F2">The Shares were called for redemption by the issuer at par value.</footnote>
    </footnotes>

    <remarks>The Shares reported herein represent Bank of America's combined holdings in multiple series of auction rate preferred securities of the issuer, which are treated herein as one class of securities in accordance with the Auction Rate Securities - Global Exemptive Relief no-action letter issued by the Securities and Exchange Commission on September 22, 2008.  The dispositions relate to CUSIP 67060D206.</remarks>

    <ownerSignature>
        <signatureName>Bank of America Corporation and Bank of America, N.A., By:/s/Michael Didovic, Title: Director</signatureName>
        <signatureDate>2011-01-20</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Merrill Lynch, Pierce, Fenner &amp; Smith Incorporated, By:/s/Lawrence Emerson, Title: Attorney-In-Fact</signatureName>
        <signatureDate>2011-01-20</signatureDate>
    </ownerSignature>
</ownershipDocument>
