N.M. Stat. § 28-2-3.1

A. If a private employer uses a written or electronic employment application, the employer shall not make an inquiry regarding an applicant's history of arrest or conviction on the employment application but may take into consideration an applicant's conviction after review of the applicant's application and upon discussion of employment with the applicant. Nothing in this section shall prohibit an employer from notifying the public or an applicant that the law or the employer's policy could disqualify an applicant who has a certain criminal history from employment in particular positions with that employer.

B. An applicant who claims to be aggrieved by a violation of Subsection A of this section may seek relief under the Human Rights Act pursuant to the process set out in Sections 28-1-10 through 28-1-13 NMSA 1978 .