Conn. Gen. Stat. § 9-224: Special election on same day as regular election.

If any special election is called to fill a vacancy in any office on the same day as a regular election, the names of the candidates for such office shall be placed on the same ballot as the names of the candidates to be voted for at such regular election, and except as otherwise specifically provided by statute, the provisions of the statutes governing regular elections shall apply to such special election.