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.