N.H. Rev. Stat. Ann. § 43:8

If in any case the whole board is disqualified the selectmen shall, in writing, so inform some justice of the superior court, who shall thereupon, with or without notice, appoint a new board for that case from qualified persons who have before holden the same office in the town, if such there be, otherwise from qualified persons, residents of another town, who have holden the same office.