If, pursuant to Section 6054.1, no election is held, the board of supervisors of the county in which the district is situated shall appoint those nominated for the offices or shall, if no person has been nominated, appoint any qualified person to the office. Any person thus appointed shall qualify, take office, and serve as if elected at a general district election.
Source:
Section 6054.2, https://leginfo.legislature.ca.gov/faces/codes_displaySection.xhtml?lawCode=HNC§ionNum=6054.2..