N.H. Rev. Stat. Ann. § 76:17-b

Whenever, after taxes have been paid, the board of tax and land appeals grants an abatement of taxes because of an incorrect tax assessment due to a clerical error, or a plain and clear error of fact, and not of interpretation, as determined by the board of tax and land appeals, the person receiving the abatement shall be reimbursed by the city or town treasurer for the filing fee paid under RSA 76:16-a, I.