Conn. Gen. Stat. § 9-210: Incompatible town offices.

No selectman shall hold the office of town clerk, town treasurer or collector of town taxes during the same official year, nor that of judge of probate for the district within which such town is located; no town treasurer shall hold the office of collector of town taxes during the same official year; nor shall any town clerk or selectman be elected a registrar of voters; and no registrar of voters shall hold the office of town clerk. No assessor shall act as a member of the board of assessment appeals. No member of the board of finance of any town shall hold any salaried town office unless otherwise provided by special act. If any registrar of voters is elected to the office of town clerk or selectman and accepts the office, he shall thereupon cease to be a registrar; and, if any town clerk or selectman is elected registrar of voters, the election shall be void; and in either of said cases the selectmen shall forthwith appoint another registrar by a writing signed by them and filed with the town clerk; but the person so appointed shall be a member of the same political party as that to which the person so elected belongs.