Cal. Health & Saf. Code § 6494
There shall be an election for assessor in each even-numbered year in which members of the board are elected, and at the same time, place, and manner; provided, however, that if a district board has elected to avail itself of the county assessment roll for district taxation pursuant to Article 6 of Chapter 7 of this part, no assessor shall thereafter be elected until it shall again elect the use of its own tax roll.
The assessor holds office for two years, and until the election and qualification of his successor except that the first assessor elected holds office until the election and qualification of his successor.
If a vacancy occurs in the office of assessor, the board shall appoint a suitable person to fill the vacancy until the next election at which an assessor may be elected under this part.
Ca. Health and Saf. Code § 6494