N.H. Rev. Stat. Ann. § 232:15

When a petition for laying out a highway is referred to the commissioners, any town in which the highway may be may present their petition to the commissioners, setting forth that the expense of the proposed highway would be excessively burdensome to them, and that another town named, situated in the vicinity, would be greatly benefited thereby, and praying that a part of the expense may be borne by such other town.