N.M. Admin. Code § 8.201.400.14
Applicants/recipients must be physically present in New Mexico and have demonstrated intent to remain in the state. If an applicant/recipient does not have the present mental capacity to declare intent, a parent, guardian, or adult child may assume responsibility for the declaration of intent. If an applicant/recipient does not have the present mental capacity to declare intent and 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. Temporary absence from the state does not prevent eligibility. A temporary absence exists when an applicant/recipient leaves the state for a specific purpose with a time-limited purpose and intends to return to New Mexico when that purpose has been accomplished. Applicants/recipients who are eligible for New Mexico medicaid are terminated if they move out of state.
N.M. Admin. Code § 8.201.400.14