A Google search on the subject provided this link: http://www.usmarriagelaws.com/search/united_states/officiants_requirements/
Although not relavent to your original question, here is what it says with regard to the Commonwealth of Massachusetts:
Ordained ministers of the gospel may perform marriages. --- Before performing marriages, ministers are required to apply for a certificate from the state. For applications write to: The Commonwealth of Massachusetts, Office of the Secretary, Supervisor, Commissions Division, State House, Boston, Massachusetts 02133. You must file a copy of your ordination certificate and a statement from the church saying that you are in good standing. Please let us know well in advance if you need a statement from us. --- Ministers must keep records of all marriages they perform. Also, ministers must return a certificate of the marriage to the town clerk or registrar who issued the marriage license and to the town clerk of the town where the marriage was performed. --- For questions see the town clerk or registrar or write to the Secretary of State.
Further down on that site, the specified requirements for New York City differ from the State of NY.