Cal. Gov't Code § 36502

(a) A person is not eligible to hold office as councilmember, city clerk, or city treasurer unless he or she is at the time of assuming the office an elector of the city, and was a registered voter of the city at the time nomination papers are issued to the candidate as provided for in Section 10227 of the Elections Code.
If, during his or her term of office, he or she moves his or her place of residence outside of the city limits or ceases to be an elector of the city, his or her office shall immediately become vacant.
(b) Notwithstanding any other provision of law, the city council of a general law or charter city may adopt or the residents of the city may propose, by initiative, a proposal to limit or repeal a limit on the number of terms a member of the city council may serve on the city council, or the number of terms an elected mayor may serve. Any proposal to limit the number of terms a member of the city council may serve on the city council, or the number of terms an elected mayor may serve, shall apply prospectively only and shall not become operative unless it is submitted to the electors of the city at a regularly scheduled election and a majority of the votes cast on the question favor the adoption of the proposal. Notwithstanding the provisions of this subdivision, the provisions of any city charter that, on January 1, 1996, impose limitations on the number of terms a member of the city council may serve on the city council, or the number of terms an elected mayor may serve, shall remain in effect. Unless otherwise prohibited by a city charter, any city charter may be amended pursuant to this section or pursuant to the procedures specified in the charter, to include the limitation authorized in this subdivision.