N.H. Rev. Stat. Ann. § 231:13

The selectmen of 2 adjoining towns, acting jointly and by a vote of the major part of each board, may lay out any new highway, or alter any existing highway within such towns, for the accommodation of the public in the same manner as selectmen are authorized to do in their respective towns; and they shall make return thereof as required in case of laying out by selectmen in their town, and cause the same to be recorded by the clerk of each of the towns.