N.H. Rev. Stat. Ann. § 482:33

If the land of any person shall be overflowed, drained or otherwise injured by the use of any dam or addition to such dam and the damage shall not, within 30 days after due notice of such damage, be satisfactorily adjusted by the party erecting or maintaining the dam or increase in such dam, either party may apply by petition to the superior court in the county or counties where such damage arises to have said damage that has been or may be done assessed.