No not automatically, and in the majority of cases, a CMA cannot legally work as a CNA without additional requirements.
A Certified Medical Assistant (no matter which national credential: AAMA, AMT, NHA, or NCCT) is not considered the legal equivalent of a Certified Nursing Assistant in most U.S. states and facilities.
The biggest barrier is federal regulation: any individual performing nurse aide duties in a Medicare- or Medicaid-certified nursing facility (virtually all skilled nursing homes) must be listed on that state’s Nurse Aide Registry. Holding a medical assistant certification alone does not place you on the registry in most states.
In the majority of states including New York, Illinois, Michigan, Pennsylvania, Ohio, Virginia, Colorado, Georgia, North Carolina, Arizona, Nevada, and many others there is no automatic approval, waiver, or reciprocity for CMAs. You are required to complete an approved CNA training program (typically 75–180 hours) and pass the state competency examination, even if you have years of experience as a medical assistant.
Only a small handful of states (California, Washington, New Jersey, Massachusetts, Oregon) currently allow nationally certified medical assistants to be added to the Nurse Aide Registry without taking the full CNA course, and even then it usually requires paperwork and proof of experience.
Hospitals and clinics sometimes hire CMAs to perform similar patient-care tasks under titles like Patient Care Technician, but they cannot legally employ you as a CNA in a nursing home setting without the state CNA credential.
Bottom line: No. In most states and in regulated long-term care facilities, a Certified Medical Assistant cannot work as a CNA until they complete the state-approved CNA training program and pass the state exam regardless of prior education or certification.