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N.H. Rev. Stat. Ann. § 661:5

United States Senator

Source. 1979, 436:1, eff

If a vacancy occurs in the office of United States senator, the governor shall fill the vacancy by temporary appointment until the next state general election, when a senator shall be elected for the unexpired term.

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.