California Code, Elections Code - ELEC § 8027

(a) Filing of nomination papers for a nonpartisan office, except for a judicial office, shall be reopened when an incumbent who is a candidate for a nonpartisan statewide, countywide, or citywide office, or for a nonpartisan office that is elected by division, area, or district which he or she currently holds at an election at which only one other candidate, excluding any write-in candidates, has qualified to have his or her name placed on the ballot for that office and either the challenger or the incumbent dies after the 88th day but before the 68th day before the election.

(b) Any person qualified to be a candidate for the office for which either the deceased challenger or the deceased incumbent was a candidate may circulate and deliver nomination papers commencing the day after the death of either the challenger or the incumbent. Candidates shall be nominated in accordance with this part, except that in-lieu-filing-fee petitions shall not be made available and nomination papers shall be returned to the elections official no later than 5 p.m. on the 68th day before the election.