N.M. Admin. Code § 8.250.400.14
An individual must physically present in New Mexico on the date of his or her application or re-determination or on the eligibility determination date and intends to remain in the state. If the applicant or re-determining recipient does not have the present mental capacity to declare intent, the parent, guardian, or adult child can assume responsibility for a declaration of intent. If there is no guardian or relative to assume responsibility for a declaration of intent, the state in which the applicant or re-determining recipient is living is recognized as the state of residence. A temporary absence from the state does not preclude eligibility. A temporary absence is considered to exist when the eligible recipient leaves the state for a specific purpose with a time-limited goal, after the accomplishment of which the eligible recipient intends to return to New Mexico. Refer to 8.200.410.12 NMAC.
N.M. Admin. Code § 8.250.400.14