N.M. Stat. § 3-15-9
Within five days after the filing with the clerk of the municipality of the charter provided for by Sections3-15-1 through 3-15-16 NMSA 1978, and the charter being approved by a majority of the members elected to the governing body of the municipality at a regular or special meeting, the presiding officer of the governing body of the municipality shall by proclamation call a special election for the purpose of submitting to the electors of the municipality the question of whether or not the municipality shall adopt the charter prepared by the charter committee. The special election may be called and held at the same time and in conjunction with the regular election for municipal officers. Should the charter filed with the clerk of the municipality fail to be approved by the governing body of the municipality, the charter shall be returned to the chairman of the charter committee together with a letter of transmittal stating the reason why the charter has been rejected by the governing body. The charter committee shall revise the charter in accordance with their instructions in the letter of transmittal and shall refile the same with the clerk of the municipality within sixty days after the chairman of the charter committee shall have had returned to him the rejected charter. If the charter is then approved, the election proclamation shall be issued, or if not approved, the charter shall be returned by the governing body to the charter committee. This procedure shall continue until a charter is presented and approved by the governing body of the municipality.
NMS § 3-15-9