N.M. Admin. Code § 10.8.2.23
The department shall conduct a state and national criminal background check, and a court records check for protective orders, of each applicant for an original, transferred or renewed license. The department shall conduct a state criminal background check, and a court records check for protective orders, for each instructor applicant for an original or renewed instructor's permit. The department may require certain applicants to provide information or execute documents to enable the department to obtain criminal history records of disposition of charges. The department may conduct such other investigation of an applicant as the department deems necessary to determine an applicant's suitability for a license or instructor's permit.
N.M. Admin. Code § 10.8.2.23