Conn. Gen. Stat. § 46b-136 (2004)
TITLE 46b FAMILY LAW CHAPTER 81St JUVENILE MATTERS
PART I GENERAL PROVISIONS
§ 46b-136. (Formerly Sec. 51-317). Appointment of attorney to represent child or youth and parent or guardian.
In any proceeding on a juvenile matter the judge before whom such proceeding is pending shall, even in the absence of a request to do so, provide an attorney to represent the child or youth, his parent or parents, guardian or other person having control of the child or youth, if such judge determines that the interests of justice so require, and in any proceeding in which the custody of a child is at issue, such judge shall provide an attorney to represent the child and may authorize such attorney or appoint another attorney to represent such child or youth, parent, guardian or other person on an appeal from a decision in such proceeding. Where, under the provisions of this section, the court so appoints counsel for any such party who is found able to pay, in whole or in part the cost thereof, it shall assess as costs against such parents, guardian, or custodian, including any agency vested with the legal custody of the child or youth, the expense so incurred and paid for by the court in providing such counsel, to the extent of their financial ability to do so.