Conn. Gen. Stat. § 9-442: When party has no registrar.

In any municipality where there is no registrar affiliated with a political party holding a primary under the provisions of sections 9-382 to 9-450, inclusive, all the powers and duties conferred by said sections upon registrars shall be exercised by both registrars of voters acting jointly. In any borough where there is no registrar affiliated with a political party holding a primary under the provisions of said sections, all the powers and duties conferred upon registrars shall be exercised by the borough clerk.