N.M. Stat. § 51-1-6
Any person who has had a continuous period of sickness or injury for which he received benefits under the Workmen's [Workers'] Compensation Act [Chapter 52, Article 1 NMSA 1978] or the New Mexico Occupational Disease Disablement Law [52-3-1 NMSA 1978] and who, in fact, has been unavailable for employment within the meaning of the Unemployment Compensation Law [Chapter 51 NMSA 1978] shall be entitled, if he was eligible before the sickness or injury occurred, to apply for and receive such unemployment compensation benefits as he would have been eligible to receive if he had been involuntarily separated from work at the time of the occurrence of the sickness or injury. The right to unemployment compensation benefits shall not be preserved under this section unless a claim for benefits is filed with respect to a week that is not later than the fourth calendar week after the termination of the continuous period of compensated sickness or injury, and unless such week is within the thirty-six month period that follows the date of the commencement of the continuous period of sickness or injury. In the event that any person has received a lump-sum award in settlement of his claim under the Workmen's [Workers'] Compensation Act or the New Mexico Occupational Disease Disablement Law, that person's continuous period of sickness or injury shall be deemed to have terminated, and he must file his claim for unemployment benefits within four weeks after the award or settlement.
NMS § 51-1-6