Cal. Civ. Proc. Code § 345

The limitations prescribed in this chapter apply to actions brought in the name of the state or county or for the benefit of the state or county, in the same manner as to actions by private parties. Accounts for the support of patients at state or county hospitals are book accounts as defined in Section 337a, and actions on them may be commenced at any time within four years after the last date of service or the last date of payment.