N.M. Stat. § 24-13-1
For the purposes of Chapter 24, Article 13 NMSA 1978, a dead body that has not been claimed by a friend, relative or other interested person assuming the responsibility for and expense of disposition shall be considered an unclaimed decedent. It is the duty of each county in this state to authorize interment or cremation of an unclaimed decedent. The county shall ensure that the body is buried or cremated no later than thirty days after a determination has been made that the body has not been claimed, but no less than fourteen days after death or discovery of the body. If the body is cremated, the county shall ensure that the cremated remains are retained and stored for at least two years, or one year for eligible veterans who qualify for veteran burial benefits, in a manner that allows for identification of the remains. After the expiration of two years, or one year for eligible veterans who qualify for veteran burial benefits, the cremated remains may be disposed of; provided the county retains a record of the place and manner of disposition for not less than five years after disposition.
NMS § 24-13-1