Under federal law, employers and universities cannot legally mandate COVID vaccines because they are unlicensed Emergency Use Authorization products that are, by definition, experimental.
In New Mexico, the Certificate of Exemption needs to include a statement or attached affidavit and be notarized. Most financial institutions will provide this service.
If you are being required to vaccinate for employment, you can use the Employment Exemption form found on the Now Exempt page.
Church of a Higher Power’s General Exemption Statement:
It is my strong religious belief that I shall not, without consent, add nor subtract anything to or from my body. Forcing this would directly violate the Free Excercise Clause and would strip me of my fundamental right to Religious Liberty.