N.Y. Fam. Ct. Act § 1042
If the parent or other person legally responsible for the child's care is not present, the court may proceed to hear a petition under this article only if the child is represented by counsel. The parent or other person legally responsible for the child's care shall be served with a copy of the order of disposition with written notice of its entry pursuant to section one thousand thirty-six of this article. Within one year of such service or substituted service pursuant to section one thousand thirty-six of this article, the parent or other person legally responsible for the child's care may move to vacate the order of disposition and schedule a rehearing. Such motion shall be granted on an affidavit showing such relationship or responsibility and a meritorious defense to the petition, unless the court finds that the parent or other person willfully refused to appear at the hearing, in which case the court may deny the motion.
N.Y. Family Court Law § 1042