N.M. Stat. § 7-1-28

A. In response to a written protest against an assessment, submitted in accordance with the provisions of Section 7-1-24 NMSA 1978 , but before any court acquires jurisdiction of the matter, or when a “notice of assessment of taxes” is incorrect, the secretary or the secretary's delegate may abate any part of an assessment determined by the secretary or the secretary's delegate to have been incorrectly, erroneously or illegally made. An abatement in the amount of twenty thousand dollars ($20,000) or more shall be made with the prior approval of the attorney general; except that the secretary or the secretary's delegate may make abatements with respect to the Oil and Gas Severance Tax Act, the Oil and Gas Conservation Tax Act, the Oil and Gas Emergency School Tax Act, the Oil and Gas Ad Valorem Production Tax Act, the Natural Gas Processors Tax Act or the Oil and Gas Production Equipment Ad Valorem Tax Act, abatements of gasoline tax made under Section 7-13-17 NMSA 1978 and abatements of cigarette tax made under the Cigarette Tax Act without the prior approval of the attorney general regardless of the amount.

B. Pursuant to the final order of the district court, the court of appeals, the supreme court of New Mexico or any federal court, from which order, appeal or review is not successfully taken by the department, adjudging that any person is not required to pay any portion of tax assessed to that person, the secretary or the secretary's delegate shall cause that amount of the assessment to be abated.

C. Pursuant to a compromise of taxes agreed to by the secretary and according to the terms of the closing agreement formalizing the compromise, the secretary or the secretary's delegate shall cause the abatement of the appropriate amount of any assessment of tax.

D. The secretary or the secretary's delegate shall cause the abatement of the amount of an assessment of tax that is equal to the amount of fee paid to or retained by an out-of-state attorney or collection agency from a judgment or the amount collected by the attorney or collection agency pursuant to Section 7-1-58 NMSA 1978 .

E. Records of abatements made in excess of ten thousand dollars ($10,000) shall be available for inspection by the public. The department shall keep such records for a minimum of three years from the date of the abatement.

F. In response to a timely protest pursuant to Section 7-1-24 NMSA 1978 of an assessment by the department and notwithstanding any other provision of the Tax Administration Act, the secretary or the secretary's delegate may abate that portion of an assessment of tax, including applicable penalties and interest, representing the amount of tax previously paid by another person on behalf of the taxpayer on the same transaction; provided that the requirements of equitable recoupment are met. For purposes of this subsection, the protest pursuant to Section 7-1-24 NMSA 1978 of the department's assessment may be made by the taxpayer to whom the assessment was issued or by the other person who claims to have previously paid the tax on behalf of the taxpayer.