Scienter or negligence, not a statute
As Dog Bite Law explains, New Mexico has no dog bite statute. A victim can recover under scienter, which makes the owner liable if the owner knew or should have known the dog was vicious, or under negligence. Courts have found that knowledge is a trigger for strict liability, not just a negligence instruction.
New Mexico uses pure comparative negligence, so your fault reduces the award. The Dangerous Dog Act regulates dogs declared dangerous, and its designations can be important evidence of negligence in a civil case.