N.M. Const. art. IV, § 4

[Terms of office of members; time of election; filling of vacancies.] Members of the legislature shall be elected as follows: those senators from Bernalillo, Chaves, Curry, DeBaca, Grant, Lea, Lincoln, Luna, Sandoval, San Juan, San Miguel, Socorro, Taos, Torrance, Union and Valencia counties for a term of six years starting January 1, 1961, and after serving such terms shall be elected for a term of four years thereafter; those senators from all other counties for the terms of four years, and members of the house of representatives for a term of two years. They shall be elected on the day provided by law for holding the general election of state officers or representatives in congress. If a vacancy occurs in the office of senator or member of the house of representatives, for any reason, the county commissioners of the county wherein the vacancy occurs shall fill such vacancy by appointment. Such legislative appointments as provided in this section shall be for a term ending on December 31, subsequent to the next succeeding general election. (As amended September 15, 1953, and November 8, 1960.)