N.Y. Dom. Law § 11
No marriage shall be valid unless solemnized by either:
A clergyman or minister of any religion, or by the senior leader, or any of the other leaders, of The Society for Ethical Culture in the city of New York, having its principal office in the borough of Manhattan, or by the leader of The Brooklyn Society for Ethical Culture, having its principal office in the borough of Brooklyn of the city of New York, or of the Westchester Ethical Society, having its principal office in Westchester county, or of the Ethical Culture Society of Long Island, having its principal office in Nassau county, or of the Riverdale-Yonkers Ethical Society having its principal office in Bronx county, or by the leader of any other Ethical Culture Society affiliated with the American Ethical Union; provided that no clergyman or minister as defined in section two of the religious corporations law, or Society for Ethical Culture leader shall be required to solemnize any marriage when acting in his or her capacity under this subdivision.
1-a. A refusal by a clergyman or minister as defined in section two of the religious corporations law, or Society for Ethical Culture leader to solemnize any marriage under this subdivision shall not create a civil claim or cause of action or result in any state or local government action to penalize, withhold benefits or discriminate against such clergyman or minister.
...
The term "clergyman" or "minister" when used in this article, shall include those defined in section two of the religious corporations law. The word "magistrate," when so used, includes any person referred to in the second or third subdivision.