Conn. Gen. Stat. § 9-169d

The legislative body of any town, consolidated town and city or consolidated town and borough which elects municipal officers from political subdivisions may establish, in accordance with the provisions of section 9-169 , for use in municipal elections and primaries, voting districts which cross congressional, senatorial or assembly district lines, but which do not cross municipal political subdivision lines, provided no special state election may be held on the same day as a regular municipal election in such municipalities.