New Mexico Statutes Chapter 24. Health and Safety § 24-5-3. Exemption from immunization

(1) a certificate of a licensed physician, a physician assistant or a certified nurse practitioner stating that the physical condition of the child is such that immunization would seriously endanger the life or health of the child;

(2) an affidavit or written affirmation from an officer of a recognized religious denomination that the child's parents or guardians are bona fide members of a denomination whose religious teaching requires reliance upon prayer or spiritual means alone for healing; or

(3) an affidavit or written affirmation from the child's parent or legal guardian that the parent's or legal guardian's religious beliefs, held either individually or jointly with others, do not permit the administration of vaccine or other immunizing agent.