N.Y. Public Health Law § 2984
3. Notwithstanding subdivision two of this section, nothing in this article shall be construed to require a private hospital to honor an agent's health care decision that the hospital would not honor if the decision had been made by the principal because the decision is contrary to a formally adopted policy of the hospital that is expressly based on religious beliefs or sincerely held moral convictions central to the facility's operating principles and the hospital would be permitted by law to refuse to honor the decision if made by the principal, provided: