N.H. Rev. Stat. Ann. § 661:1

Vacancies Generally

Source. 1979, 436:1, eff

Any vacancy as defined in RSA 652:12 in a public office voted for at any state election shall be filled according to the provisions of this chapter.

Official source: New Hampshire General Court. Reproduced from public-domain New Hampshire statutes; confirm against the official source for the current text. Not legal advice.