Section 235 - Compensation and liability for support and care in counties within the city of New York(a) Upon the detention, placement or commitment of a child by the family court in a county within the city of New York to a public or private institution other than a shelter maintained and conducted by a society for the prevention of cruelty to children, the department of social services of the city of New York shall investigate the ability of the parent of the child, or other person legally chargeable, to contribute in whole or in part to the expense incurred by the city of New York on account of the maintenance of such child.(b) If in the opinion of the department of social services such parent or legal custodian is able to contribute in whole or in part the commissioner of social services shall thereupon institute a proceeding in the family court to compel such parent or person legally chargeable to contribute such portion of such expense on account of maintenance of such child as shall be proper and just.N.Y. Family Court Law § 235