You need to obtain a divorce from the Supreme Court in New York—the New York court system’s highest court is the Court of Appeals, so the Supreme Court in the state is not the equivalent of the federal Supreme Court and is more like a district or county court in other states.
You should file for divorce with the Supreme Court in the county where either you live or where your spouse lives currently. The NYCourts Court Locator can help you to determine where you should file.
You must buy an Index Number at the County Clerk’s Office to initiate divorce proceedings and must file required legal documents including a Summons with Notice or a Summons with Verified Complaint.
Your spouse must be served with divorce papers and provided with the opportunity to respond to the court.