N.M. Stat. § 72-12-12
It shall be unlawful for any person, firm or corporation to drill or to begin the drilling of a well for water from an underground stream, channel, artesian basin, reservoir or lake (hereinafter referred to as "underground source") the boundaries of which have been determined and proclaimed by the state engineer of New Mexico to be reasonably ascertainable, without a valid, existing license for the drilling of such wells issued by the state engineer of New Mexico in accordance with the provisions of this act [72-12-12 to 72-12-17 NMSA 1978], and the rules and regulations promulgated by him in pursuance hereof. Such licenses shall not be required for the construction of a driven well; provided, that the casing for such well shall not exceed two and three-eighths inches outside diameter.
NMS § 72-12-12