Conn. Gen. Stat. § 9-220: Town office.

If any town office in any town is vacant from any cause, such town, if such office is elective, shall, except as otherwise provided by law, fill the vacancy at the next town election or at a special election called for such purpose in accordance with the provisions of section 9-164, but, until such vacancy is so filled, it shall be filled by the selectmen. The selectmen shall fill all vacancies in offices to which they have the power of appointment.