N.Y. Fam. Ct. Act § 415
Except as otherwise provided by law, the spouse or parent of a recipient of public assistance or care or of a person liable to become in need thereof or of a patient in an institution in the department of mental hygiene, if of sufficient ability, is responsible for the support of such person or patient, provided that a parent shall be responsible only for the support of his child or children who have not attained the age of twenty-one years. In its discretion, the court may require any such person to contribute a fair and reasonable sum for the support of such relative and may apportion the costs of such support among such persons as may be just and appropriate in view of the needs of the petitioner and the other circumstances of the case and their respective means. Step-parents shall in like manner be responsible for the support of children under the age of twenty-one years.
N.Y. Family Court Law § 415