N.H. Rev. Stat. Ann. § 49-C:29

Written notice of election or appointment of any city officer shall be mailed to him at his address by the city clerk within 48 hours after the appointment is made or the vote canvassed. If, within 10 days from the date of the notice, such officer shall not take, subscribe to, and file with the city clerk an oath of office, such neglect shall be deemed a refusal to serve and the office shall be deemed vacant, unless the elected body shall extend the time in which such officer may qualify.