California Code, Health and Safety Code - HSC § 40225

No supervisor, mayor, or city council member shall hold office on the bay district board for a period of more than three months after ceasing to hold the office of supervisor, mayor, or city council member, respectively, and his or her membership on the bay district board shall thereafter be considered vacant, except that any mayor who continues to hold office as a city council member, or any city council member who continues to hold office as a mayor, shall not be considered to have ceased to hold office under this section.