N.H. Rev. Stat. Ann. § 76:6

In assessing such taxes the selectmen may assess a sum not exceeding 5 percent more than the amount of such tax, to answer any abatements that may be made, which shall be paid into the town treasury for the use of the town. But if the selectmen shall assess a sum exceeding that which they have a right to assess, such assessment shall be thereby rendered invalid only as to such excess.