N.M. Stat. § 3-7-2
A municipal utility or a utility under the jurisdiction of the New Mexico public utility commission and having a franchise from the municipality may extend service to territory annexed by the municipality. If the territory annexed to the municipality is being served by a utility under the jurisdiction of the New Mexico public utility commission and the municipality is being served by another utility under the jurisdiction of the New Mexico public utility commission, the New Mexico public utility commission shall determine which utility under its jurisdiction shall serve the territory annexed to the municipality. The municipality shall grant a franchise to the utility that is to serve the territory annexed to provide utility service in the territory annexed upon such terms as are fair, just and equitable to all parties concerned.
NMS § 3-7-2