California Code, Elections Code - ELEC § 7557

(a) If the vacancy occurs in a senatorial or Assembly district situated wholly within the limits of a single county, by appointment by the county central committee of the party in the county.  Whenever a vacancy occurs by reason of the failure to nominate a person affiliated with the party, no person shall be chosen to fill the vacancy who does not reside in the senatorial or Assembly district involved.

(b) If the vacancy occurs in a senatorial or Assembly district comprising two or more counties, parts of two or more counties, or one or more counties and parts of one or more counties, by appointment by the county central committee representing more voters affiliated with the American Independent Party than does any other county central committee in the district.

(c) If there is no county central committee qualified to act, or the qualified county central committee fails to act, under the provisions of subdivision (a) or (b) of this section, the appointment shall be made by the state central committee of the party.

(d) If the vacancy occurs as to a delegate for a United States Senator from California or as to a delegate for any of the state officers named in Section 7550 by appointment by the state central committee of the party.

(e) If the vacancy occurs as to a delegate for any Representative in Congress from California, by appointment by the state central committee of the party of a voter who resides within the congressional district to be represented.