N.H. Rev. Stat. § 21-J:31

Any taxpayer who fails to file a return when due, unless an extension has been granted by the department, shall pay a penalty equal to 5 percent of the amount of the tax due or $10, whichever is greater, for each month or part of a month during which the return remains unfiled. The total amount of any penalty shall not, however, exceed 25 percent of the amount of the tax due or $50, whichever is greater. This penalty shall not be applied in any case in which a return is filed within the extended filing period as provided in RSA 77-A:9, RSA 77-E:8, RSA 83-C:6, RSA 84-A:7, or RSA 84-C:7, or the failure to file was due to reasonable cause and not willful neglect of the taxpayer. The amount of the penalty is determined by applying the percentages specified to the net amount of any tax due after crediting any timely payments made through estimating or other means.