N.H. Rev. Stat. Ann. § 80:57

If any person tenders a payment for any taxes and/or interest, in excess of the taxes levied and interest incident thereto, the collector of taxes shall direct the selectmen to issue an order upon the town treasurer to refund to the person making such payment or his heirs or assigns the excess sum so paid; provided, however, that if the sum overpaid is $5 or less, no refund shall be required unless the taxpayer in such case shall apply in writing to the tax collector for said refund within 60 days of actual payment.