Cal. Welf. and Inst. Code § 634
When it appears to the court that the minor or his or her parent or guardian desires counsel but is unable to afford and cannot for that reason employ counsel, the court may appoint counsel. In a case in which the minor is alleged to be a person described in Section 601 or 602, the court shall appoint counsel for the minor if he or she appears at the hearing without counsel, whether he or she is unable to afford counsel or not, unless there is an intelligent waiver of the right of counsel by the minor. In any case in which it appears to the court that there is such a conflict of interest between a parent or guardian and child that one attorney could not properly represent both, the court shall appoint counsel, in addition to counsel already employed by a parent or guardian or appointed by the court to represent the minor or parent or guardian. In a county where there is no public defender, the court may fix the compensation to be paid by the county for service of that appointed counsel.
Ca. Welf. and Inst. Code § 634