N.H. Rev. Stat. Ann. § 234:38

The selectmen of a town or the mayor of a city, may, by appropriate barriers and signs, temporarily close or regulate travel on any class IV or class V highway or bridge thereon, in order to perform work on such highway or bridge, and may establish, maintain and mark detours. Any person who travels on such closed highway or bridge, or who violates the provisions of such regulations, shall be fined not more than $100.