Section 234 - Compensation and liability for support and care in counties outside the city of New York(a) Whenever a child is detained, placed or committed under the provisions of this act to an authorized agency, or to any person other than his parent and is retained in accordance with the rules of the state board of social welfare, compensation for his care and maintenance shall be a charge on the county. The compensation paid by the county for care and maintenance of the child may be charged back to a city or town in the county in accordance with and to the extent permitted by the provisions of the social services law. All bills for such care and maintenance to be paid from public funds shall be paid by the county treasurer from moneys appropriated for public assistance and care in the county social services district by warrant of the commissioner of social services.(b) The court may, after issuance and service of an order to show cause upon the parent or other person having the duty under the law to support such child, adjudge that such parent or other person shall pay to the court such sum as will cover in whole or in part the support of such child, and willful failure to pay such sum may, in the discretion of the court, be punished as for a criminal contempt of court. When a person liable to such payment on order, as herein provided, is before the court in the proceeding relating to the commitment or placement, a formal order to show cause may be dispensed with in the discretion of the court.(c)(i) The social services district from which the detention, placement or commitment is made shall be entitled to be reimbursed by another social services district for its expenditures for care and maintenance of the child, if, and to the extent that, it would have been entitled to be reimbursed therefor by such other district had the care been provided under and pursuant to the provisions of the social services law. The commissioner of social services of the social services district from which the commitment was made may enforce repayment from the other social services district in accordance with the provisions of the social services law.(ii) In accordance with the provisions of the social services law and the rules and regulations of the state department of social services relating to state charges, and from funds available to the state department of social services therefor, the state shall reimburse the social services district for the full cost of care and maintenance of the child, in the event the child is a state charge as defined by the social services law.N.Y. Family Court Law § 234