Conn. Gen. Stat. § 9-393: Selection of town committee members and delegates.

All town committee members and delegates to conventions shall be chosen as provided in sections 9-382 to 9-450, inclusive. Vacancies in town committees, arising from any cause including failure to elect, shall be filled in such manner as the rules of the party prescribe. The chairman of a town committee may be chosen by the town committee from within or without the membership of the town committee as the rules of the party prescribe. Any town committee may, by party rules adopted in accordance with section 9-375 and filed under section 9-374, increase its membership and fill new positions created by such increase in the manner prescribed in the applicable party rules. The rules of a party may provide methods for the filling of vacancies in delegations to conventions, which methods may include prescribing that each delegate selected in conformity with the provisions of sections 9-382 to 9-450, inclusive, may designate an alternate delegate or a proxy to act for him in his absence.