N.H. Rev. Stat. Ann. § 234:12

When a bridge crosses the boundary line between 2 municipalities within the state, the 1/5 cost to be borne by a municipality pursuant to RSA 234:10 shall be borne by the 2 municipalities in proportion to their last equalized valuations, unless by mutual concurrence the 2 municipalities agree to some other financial arrangement to provide the required share of cost.