California Code, Elections Code - ELEC § 8140

Any candidate for a nonpartisan office who at a primary election receives votes on a majority of all the ballots cast for candidates for that office shall be elected to that office.  Where two or more candidates are to be elected to a given office and a greater number of candidates receive a majority than the number to be elected, those candidates shall be elected who secure the highest votes of those receiving a majority, and equal in number to the number to be elected.

Where a candidate has been elected to a nonpartisan office at the primary election, that office shall not appear on the ballot at the ensuing general election, notwithstanding the death, resignation, or other disqualification of the candidate at a time subsequent to the primary election.