Both spouses must agree on all matters, such as child custody, maintenance, and property division, in order to petition for an uncontested divorce in New York. Submit the required documents, such as a divorce petition and marriage settlement agreement, to your county's Supreme Court. Both parties must file additional filings, such as an affidavit of defendant's default, after serving your spouse with the divorce papers. After examining the paperwork, the court will decide whether to grant the divorce.