N.M. Stat. § 77-16-11
When any animal, of whatsoever class or species it may be, [shall] break, obstruct or injure any rail, post, stake or any material of which a fence is constructed, the owner of such animal shall be compelled to pay the damages occasioned to the owner of the fence, according to the damages sustained and suffered: provided, that if any animal be taken near any fence, and it shall result in his injuring it, then the person who ordered the animal to be placed there shall pay the damage, and if the herder who has the care of the animal, shall take them there without order from the owner of them, in such case, the father, mother or guardian of him who drove the animals there, if the herder be a minor, shall pay the damages, and if he be of age, he himself shall pay it when he does it without the express order of the owner.
NMS § 77-16-11