N.M. Stat. § 29-2-7
The New Mexico state police shall cause all applicants for the position of commissioned officer to submit a written detailed application on forms as the secretary shall prescribe, and the secretary shall cause an investigation to be made of all applicants, subsequent to their taking the examination referred to in Section 29-2-8 NMSA 1978, for the purpose of determining the moral character, general reputation and fitness of any applicant. An applicant who is found unfit as a result of the investigation shall be disqualified for employment. The secretary shall by rule prescribe the physical qualifications of applicants and shall require each applicant to submit to a physical examination by doctors as the secretary shall designate. An applicant who does not meet the physical requirements prescribed by the secretary shall be disqualified for employment. Inasmuch as laws have been enacted providing for retirement, disability and life insurance funds for members of the New Mexico state police, it is the intention of the legislature that no applicants will be appointed who are in such physical condition that the cost of such protection will thereby be increased.
NMS § 29-2-7