N.M. Stat. § 12-3-15
The "statuary hall commission" is created. The commission shall be composed of no more than nine persons, the chairman of which shall be the governor and the membership of which shall include the state treasurer, the state cultural affairs officer, the executive director of the New Mexico office of Indian affairs [Indian affairs department] and no fewer than four members appointed by the governor from a list of names that have been submitted to him by the Indian nations, tribes or pueblos in New Mexico, containing names of members of those Indian nations, tribes or pueblos who would be appropriate to serve on the commission. Terms of the members shall extend until a second statue from New Mexico is emplaced in the national statuary hall in Washington, D.C. The governor shall fill any vacancy on the statuary hall commission within three months from the date that the vacancy occurs in the same manner as original members were appointed.
NMS § 12-3-15