N.M. Stat. § 28-1-4

A. The commission may:

(1) hear complaints and issue orders, including cease and desist orders concerning alleged unlawful discriminatory practice;

(2) hold hearings, subpoena witnesses and compel their attendance, administer oaths, take the testimony of any person under oath, order depositions and require the production for examination of any books, records, correspondence, documents and other evidence relating to any matter under investigation or in question before the commission. Contumacy or refusal to obey a subpoena issued pursuant to this section constitutes contempt punishable by the district court of the judicial district in which the witness may be found. No individual shall be excused from attending and testifying or from producing evidence in obedience to a subpoena issued pursuant to this section on the grounds that the testimony or evidence required of him may tend to incriminate him or subject him to a penalty or a forfeiture. However, no individual shall be prosecuted or subjected to any penalty or forfeiture concerning any matter for which he is compelled to testify or give evidence after having claimed his right against self-incrimination. Nevertheless, the individual so testifying shall not be exempt from prosecution and punishment for perjury committed while testifying.

B. The division may:

(1) receive and investigate complaints of alleged unlawful discriminatory practice;

(2) seek to eliminate discrimination through conciliation and persuasion by voluntary conferences with interested parties;

(3) recommend application by the director to a district court in the county where the violating party resides for specific performance of any conciliation agreement or for enforcement of any order issued by the commission;

(4) endeavor to eliminate prejudice and to further good will. The division in cooperation with the state department of public education and local boards of education shall encourage an educational program for all residents of the state, calculated to eliminate prejudice, its harmful effects and its incompatibility with principles of fair play, equality and justice;

(5) encourage voluntary advisory groups to study problems of discrimination in all fields, to foster, through community efforts, good will and cooperation in this state and to make recommendations to the secretary for the development of policies and procedures which the secretary may recommend to appropriate state agencies;

(6) seek and enlist the cooperation and contributions and grants of individuals and foundations, private, charitable, religious, labor, civic and benevolent organizations and the federal government for the purposes of this section;

(7) issue publications and release the results of investigation and research which in the secretary's judgment will tend to promote good will and prevent or eliminate discrimination; and

(8) submit annually a written report of all its activities and recommendations to the secretary, the governor and the legislature.