N.M. Stat. § 17-4-15
Except as in this division otherwise provided, all game and fish, with the natural increase thereof, held or confined in any private preserve, park or lake, licensed under the provisions of this act shall, during the existence of the license or any renewal thereof, be deemed the property of the licensee of the same to the extent that he may lawfully retain, pursue, capture, kill, use, sell or dispose of the game or fish therein in any quantity, in any manner and at any time of the year, and the pursuit, capture, wounding or killing of any game or fish in any licensed preserve, park or lake, public or private, without the consent of the proprietor, shall be unlawful; provided, that the aggregate number of game animals or fish in any licensed private preserve, park or lake, which contained game or fish belonging to the state at the time or date of the issuing of such license, shall not be lessened by the killing, use, sale or disposition thereof, it being the purpose of this provision to restrict such killing, use, sale and disposition to a number not exceeding in the aggregate the natural increase. If by reason of controlling necessity or for the purpose of stocking or replenishing some other park or lake, any proprietor of a licensed preserve, park or lake may desire to lessen the aggregate number above provided for, the state game and fish warden [director of the department of game and fish] may, on being satisfied of the property [propriety] thereof, grant a permit therefor.
NMS § 17-4-15