N.H. Rev. Stat. Ann. § 231:44

When any class IV, V or VI highway, which joins a highway in another town, has been discontinued by vote of the town, the selectmen of the town wherein the highway has been so discontinued shall notify the selectmen of said adjoining town, by registered mail, of the fact of said discontinuance. Said notification shall be made within 15 days after the action of discontinuance has been taken.