N.H. Rev. Stat. Ann. § 149-I:7

The mayor and aldermen may assess upon the persons whose drains enter such main drains, common sewers, stormwater treatment, conveyance, and discharge systems, or treatment facilities, or whose lands receive special benefit therefrom in any way, their just share of the expense of constructing and maintaining the same or paying off any capital debt or interest incurred in constructing and/or maintaining the same.