California Code, Elections Code - ELEC § 11302

(b)(1) Upon the occurrence of the vacancy, the elections official for each county in which a section of the recall petition has been filed shall immediately verify the signatures on the petition submitted to the elections official as of the date of the vacancy.

(2) If the elections official verifies that a sufficient number of signatures were filed as of the date of the vacancy, the recall election shall proceed.

(3) If the elections official verifies that an insufficient number of signatures, or no signatures, were filed as of the date of the vacancy, the recall election shall not proceed and a vacancy in the office that is the subject of the recall election shall be filled as otherwise provided by law.

(4) A person who was subject to a recall petition may not be appointed to fill the vacancy in the office that he or she vacated and that person may not be appointed to fill any other vacancy in office on the same governing board for the duration of the term of office of the seat that he or she vacated.