Conn. Gen. Stat. § 9-216: Nomination by petition.

Nominations may also be made by petition in vacancy elections for the offices of state senator and state representative in the manner provided in sections 9-379 and 9-453a to 9-453p, inclusive, which petitions shall be submitted to the town clerk of the town in which the signers reside not later than eight days after the issue of such writs as provided in section 9-215 and filed in the office of the Secretary of the State not later than two days thereafter.