N.H. Rev. Stat. Ann. § 231:26

The selectmen of such town may agree as to the proportion of expense to be borne by each town in such purchase, and in the construction and maintenance of a highway over said river, including a bridge and the piers, abutments and approaches thereto, and as to the proportion which each town shall contribute towards the payment of damages to third persons injured in the use of such highways, subject to the approval of the town; and any contract executed between the selectmen of such towns shall be legal and binding when approved by the towns directly interested therein, or if made under the authority of such towns.