The State of New York does not allow individuals of the same sex to legally marry. However, if individuals of the same sex entered into a valid marriage in another state and are New York residents, meeting the jurisdictional requirements of New York Domestic Relations Law, they can still obtain a divorce in New York. In the case of Dickerson v. Thomson, the Third Department of the Appellate Division (an appeals court) held that New York State courts have subject matter jurisdiction to deal with divorces arising out of same-sex relationships.
In the Dickerson case, the parties had entered into a a civil union in the state of Vermont. By the time the civil union failed, both of the parties had moved out of Vermont and were now New York residents. The State of New York recognized the civil union made in Vermont based on comity (respect for the laws of a different state). The proceeding to dissolve the civil union was brought in the State of New York.