N.M. Stat. § 72-1-1
Natural waters; public.
All natural waters flowing in streams and watercourses, whether such be perennial,
or torrential, within the limits of the state of New Mexico, belong to the public and are
subject to appropriation for beneficial use. A watercourse is hereby defined to be any
river, creek, arroyo, canyon, draw or wash, or any other channel having definite banks
and bed with visible evidence of the occasional flow of water.