N.H. Rev. Stat. Ann. § 75:15

If the assessing officials deny in whole or in part any application for classification as an eligible residence, the applicant, having complied with the requirements of RSA 75:11, I, may, within 6 months after notice of denial or classification, apply by petition to the superior court of the county, which shall make such order thereon as justice requires. Any appeal to the superior court under this section shall be in lieu of an appeal to the board of tax and land appeals pursuant to RSA 75:14.