N.Y. Domestic Relations Law § 113
3.
(ii) In any other agency adoption proceeding, the petition shall be filed in the same court and, wherever practicable, shall be assigned to the same judge of the county in which parental rights had been terminated, a judicial surrender had been approved or the most recent proceeding under article ten or ten-A of the family court act or section three hundred fifty-eight-a of the social services law had been heard, whichever occurred last, or in the county where the adoptive parents reside or, if such adoptive parents do not reside in this state, in the county where such authorized agency has its principal office. The following procedures shall be applicable in cases where the child is under the jurisdiction of a family court, but where the adoption petition has been filed in a court other than the court that presided over the termination of parental rights, surrender or most recent proceeding under article ten or ten-A of the family court act or section three hundred fifty-eight-a of the social services law, whichever occurred last: