N.H. Rev. Stat. Ann. § 232:17

If the commissioners decide to lay out the highway they may in their report apportion and assign such part of the damages assessed and of the expense of laying out and making the highway, including bridges thereon, and of the cost of their future repair and maintenance, as they think just, to be paid by such other town; and upon acceptance of such report and judgment thereon such other town shall at all times contribute the amount apportioned or be liable therefor.