N.H. Rev. Stat. Ann. § 231:52

The mayor and aldermen of a city or the selectmen of a town may release and discharge any way dedicated as aforesaid from all public servitude at any time after such dedication, upon petition by any interested party and notice and hearing thereon, whenever in their opinion such way will not be needed for the accommodation of public travel. All proceedings shall be conducted in the manner provided for the laying out of highways, and any interested party may appeal to the superior court from the decision, as in the case of petitions for laying out highways.