N.H. Rev. Stat. § 660:25
If 2 or more candidates for United States representative in any district or United States senator shall receive the largest and equal number of votes in any state general election so that no choice is made, the governor, with advice of the council, shall cause precepts to be issued to the selectmen of the several towns within such district for another election, requiring them to warn meetings to be held at the time specified in such precepts for the choice of a representative or senator. The votes given at any such meeting shall be received, sorted, counted, declared, recorded and certified, and the returns thereof made out, signed, certified, sealed, directed and forwarded in the manner prescribed by RSA 659.
RSA 660:25
1979, 436:1. 1987, 276:1, eff. July 24, 1987.