RSA 669:64: Supervisors of the Checklist.

Vacancies in the board of supervisors shall be filled within 45 days by appointment made by the remaining supervisors. If there is only one member of the board, or if the whole board shall be vacant, or if the remaining supervisors fail to fill the vacancy within 45 days, the moderator shall make the appointments. If a town elects supervisors by means of the partisan ballot system, any such appointee shall be of the same political party as the supervisor whose place he is filling.