N.H. Rev. Stat. § 77:24
The department of revenue administration shall reassess the amount of the tax in every case in which it appears in the examination of the returns that the amount paid is either higher or lower than the actual tax due. The department shall notify the taxpayer of any corrections made. If the department of revenue administration determines a deficiency, the amount of said deficiency and interest as prescribed in RSA 21-J:28 shall be forwarded by the taxpayer to the department of revenue administration within 15 days from the date of the required notice. If the reassessment results in a determination of overpayment, the amount of the excess shall be repaid to the taxpayer in the manner provided by RSA 21-J:28-a. All assessments made under this section shall be subject to the same right of appeal as provided in RSA 21-J:28-b, and nothing contained in this section shall be construed to limit the power of the commissioner of revenue administration to make a later assessment under RSA 21-J:29 and to seek penalties for fraudulent returns as provided by RSA 77:30.
RSA 77:24
1950, 5, part 8:15. RSA 77:24. 1973, 544:11, IV. 1975, 439:24. 1981, 314:9; 465:2. 1982, 42:96. 1983, 441:2. 1985, 204:9. 1991, 163:14, eff. May 27, 1991.