Exhibit g.3

NUVEEN CONNECTICUT PREMIUM INCOME MUNICIPAL FUND

RENEWAL OF INVESTMENT MANAGEMENT AGREEMENT

This Agreement made this 28th day of May 2009 by and between Nuveen Connecticut Premium Income Municipal Fund, a Massachusetts business trust (the “Fund”), and Nuveen Asset Management, a Delaware corporation (the “Adviser”);

WHEREAS, the parties hereto are the contracting parties under that certain Investment Management Agreement (the “Agreement”) pursuant to which the Adviser furnishes investment management and other services to the Fund; and

WHEREAS, the Agreement terminates August 1, 2009 unless continued in the manner required by the Investment Company Act of 1940; and

WHEREAS, the Board of Trustees, at a meeting called for the purpose of reviewing the Agreement, have approved the Agreement and its continuance until August 1, 2010 in the manner required by the Investment Company Act of 1940.

NOW THEREFORE, in consideration of the mutual covenants contained in the Agreement the parties hereto do hereby continue the Agreement in effect until August 1, 2010 and ratify and confirm the Agreement in all respects.

NUVEEN CONNECTICUT PREMIUM INCOME MUNICIPAL FUND
By:	/s/ Mark L. Winget
	Vice President

ATTEST:

/s/ Virginia O’Neal

Assistant Secretary

NUVEEN ASSET MANAGEMENT
By:	/s/ William T. Huffman
	Managing Director

ATTEST:

/s/ Christopher Rohrbacher

Assistant Secretary