N.M. Stat. § 17-5-4
The state game commission is authorized and directed to administer the provisions of Sections17-5-1 through 17-5-9 NMSA 1978, and to make such rules and regulations and establish such service as it may deem necessary to carry out all the provisions and purposes of those sections. In making such rules and regulations and providing when and by what means fur-bearing animals may be hunted, taken, captured, possessed or killed, the state game commission shall give due regard to the zones of temperatures and to the distribution, abundance, economic value and breeding habits of such animals. Provided, nothing in Sections17-5-1 through 17-5-9 NMSA 1978 shall interfere with the authority granted to the president of New Mexico state university under Sections77-15-1 through 77-15-5 NMSA 1978, or shall prevent livestock producers without a permit from the taking of bobcats that are doing damage to livestock.
NMS § 17-5-4