RSA 197:26: Vacancies.

The school board shall fill vacancies occurring on the board, and in other district offices, except that of moderator, until the next annual meeting of the district. In case of vacancy of the entire membership of the board, or the remaining members are unable to agree upon an appointment, the selectmen, upon application of one or more voters in the district, shall fill the vacancies so existing until the next annual meeting of the district.