N.H. Rev. Stat. § 21-J:28-a

I. Except as otherwise provided by law, any claim for refund or credit of overpayment of taxes administered by the department shall be filed with the department in writing in such form as the department may by rule prescribe, and shall state the specific grounds upon which it is founded. II. After a claim for refund is filed, the department shall examine it and either issue the refund or grant the credit to the claimant, or issue a notice of complete or partial denial. After receipt of the department's decision, the claimant may file a written petition for reconsideration with the department as provided in RSA 21-J:28-b. III. With respect to any refund claim filed with the department pursuant to this section, the commissioner and the taxpayer may, in writing, agree to extend the time for action upon such claim for refund. IV. In the case of any refund or credit of more than $10 for overpayment of taxes administered by the department, the department shall apply the refund or credit as an offset to any liability with respect to any tax administered by the department. The department shall notify the taxpayer in the event of any such offset in tax. V. In all cases where it appears that a taxpayer has overpaid his or her tax and the overpayment is $10 or less, the department may, in its discretion, disregard the overpayment if the cost to the state to refund the overpayment would exceed the amount involved, unless the taxpayer has requested the refund. VI. The procedure outlined in this section and in RSA 21-J:28-b shall be the exclusive method by which taxpayers may challenge their liability for any tax, or the application to them of any provision of this chapter.