N.M. Admin. Code § 8.240.400.14
An applicant/recipient must be physically present in New Mexico on the date of application or final determination of eligibility and have demonstrated intent to remain in the state. If the applicant/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 where the applicant/ recipient is living is recognized as the state of residence. A temporary absence from the state does not prevent eligibility. A temporary absence exists if an applicant/ recipient leaves the state for a specific purpose with a time-limited goal and intends to return to New Mexico when the purpose is accomplished.
N.M. Admin. Code § 8.240.400.14