N.Y. Dom. Rel. Law § 12
No particular form or ceremony is required when a marriage is solemnized as herein provided by a clergyman or magistrate, or one-day marriage officiant as designated by a town or city clerk pursuant to section eleven-d of this article, but the parties must solemnly declare in the presence of a clergyman, magistrate, or such one-day marriage officiant and the attending witness or witnesses that they take each other as spouses. In every case, at least one witness beside the clergyman, magistrate, or such one-day marriage officiant must be present at the ceremony.
The preceding provisions of this chapter, so far as they relate to the manner of solemnizing marriages, shall not affect marriages among the people called friends or quakers; nor marriages among the people of any other denominations having as such any particular mode of solemnizing marriages; but such marriages must be solemnized in the manner heretofore used and practiced in their respective societies or denominations, and marriages so solemnized shall be as valid as if this article had not been enacted.
N.Y. Dom. Rel. Law § 12