California Code, Elections Code - ELEC § 15460

In each county the number of candidates for membership in a county central committee in each Assembly or supervisorial district who receive the highest number of votes shall be declared elected.  However, a candidate for membership shall not be declared elected unless he or she has received votes equal in number to the minimum number of signatures to the nomination paper which would have been required to place his or her name on the direct primary ballot as a candidate for member of a committee.