N.M. Stat. § 10-5-8
Whenever the secretary of finance and administration assumes control of any office as hereinabove provided, the secretary may assign any employee of the department of finance and administration to perform the duties of the official suspended by the secretary.
The secretary of finance and administration may reinstate a suspended official of any local public body whenever the suspended official has made a proper showing satisfactory to the secretary that he is able and willing to conduct his office as provided by law, and that no loss will be suffered by the local public body.
In all cases where there shall be grounds for removal of such official, the secretary of finance and administration may cause removal proceedings to be instituted and prosecuted by the attorney general or district attorney, in the manner now provided by law for the institution and prosecution of such proceedings by the district attorney.
NMS § 10-5-8