N.M. Code R. § 4.10.7.14
When a state agency which has direct or indirect jurisdiction over any land or structure modification which may affect a registered cultural property does not concur with a determination proposed consistent with 4.10.7.10 NMAC above, the head of such agency may appeal to the cultural properties review committee with a statement of the case in appropriate detail. Such appeal shall be made not less than 30 days before a scheduled committee meeting. The committee shall hear the case in a regular public meeting and shall have authority (1) to request further information, (2) to accept the determination of the state agency or of the state historic preservation officer, or (3) to specify another solution consistent with its established and written standards. Appeal to the cultural properties review committee shall be the final administrative appeal in any case.
N.M. Code R. § 4.10.7.14