California Code, Probate Code - PROB § 2920

(a) If any person domiciled in the county requires a guardian or conservator and there is no one else who is qualified and willing to act and whose appointment as guardian or conservator would be in the best interests of the person, then either of the following shall apply:

(b) The public guardian shall apply for appointment as guardian or conservator of the person, the estate, or the person and estate, if the court so orders. The court may make an order under this subdivision on motion of an interested person or on the court's own motion in a pending proceeding or in a proceeding commenced for that purpose. The court shall order the public guardian to apply for appointment as guardian or conservator of the person, the estate, or the person and estate, on behalf of any person domiciled in the county who appears to require a guardian or conservator, if it appears that there is no one else who is qualified and willing to act, and if that appointment as guardian or conservator appears to be in the best interests of the person. However, if prior to the filing of the petition for appointment it is discovered that there is someone else who is qualified and willing to act as guardian or conservator, the public guardian shall be relieved of the duty under the order. The court shall not make an order under this subdivision except after notice to the public guardian for the period and in the manner provided for in Chapter 3 (commencing with Section 1460) of Part 1, consideration of the alternatives, and a determination by the court that the appointment is necessary. The notice and hearing under this subdivision may be combined with the notice and hearing required for appointment of a guardian or conservator.

(c) The public guardian shall begin an investigation within two business days of receiving a referral for conservatorship or guardianship.