New Hampshire Statutes § 669:63 Selectmen

Vacancies in the board of selectmen shall be filled by appointment made by the remaining selectmen. Whenever the selectmen fail to make such appointment, the superior court or any justice thereof, on petition of any citizen of the town, and after such notice as the court shall deem reasonable, may appoint a suitable person to fill the vacancy; provided, however, that if the town has adopted the provisions of RSA 669:61 , IV , and a petition thereunder is submitted before the submission of a petition under this section, the provisions of RSA 669:61 , IV shall apply.