N.H. Rev. Stat. Ann. § 231:33

After the betterments authorized by RSA 231:28 have been completed by a town, the highway agent or other duly authorized official under the direction of the selectmen shall have charge of all further repair and maintenance of such highways, streets, roads and traveled ways, and such highways shall be maintained, repaired and reconstructed by the town in which they are located without further assessment of the owners of property abutting or served by said facilities.