GOV §36512: (a) If a vacancy occurs in an appointive office provided for in this chapter, the council shall fill the vacancy by appointment.

(a) If a vacancy occurs in an appointive office provided for in this chapter, the council shall fill the vacancy by appointment. A person appointed to fill a vacancy holds office for the unexpired term of the former incumbent. (b) If a vacancy occurs in an elective office provided for in this chapter, the council shall, within 60 days from the commencement of the vacancy, either fill the vacancy by appointment or call a special election to fill the vacancy. (1) If the council calls a special election, the special election shall be held on the next regularly established election date not less than 114 days from the call of the special election. A person elected to fill a vacancy holds office for the unexpired term of the former incumbent. (2) If the council fills the vacancy by appointment, the person appointed to fill the vacancy shall hold office pursuant to one of the following: (A) If the vacancy occurs in the first half of a term of office and at least 130 days prior to the next general municipal election, the person appointed to fill the vacancy shall hold office until the next general municipal election that is scheduled 130 or more days after the date the council is notified of the vacancy, and thereafter until the person who is elected at that election to fill the vacancy has been qualified. The person elected to fill the vacancy shall hold office for the unexpired balance of the term of office. (B) If the vacancy occurs in the first half of a term of office, but less than 130 days prior to the next general municipal election, or if the vacancy occurs in the second half of a term of office, the person appointed to fill the vacancy shall hold office for the unexpired term of the former incumbent. (c) Notwithstanding subdivision (b) and Section 34902, a city may enact an ordinance that does any of the following: (1) Requires that a special election be called immediately to fill every city council vacancy and the office of mayor designated pursuant to Section 34902. The ordinance shall provide that the special election shall be held on the next regularly established election date not less than 114 days from the call of the special election. (2) Requires that a special election be held to fill a city council vacancy and the office of mayor designated pursuant to Section 34902 when petitions bearing a specified number of verified signatures are filed. The ordinance shall provide that the special election shall be held on the next regularly established election date not less than 114 days from the filing of the petition. A governing body that has enacted such an ordinance may also call a special election pursuant to subdivision (b) without waiting for the filing of a petition. (3) Provides that a person appointed to fill a vacancy on the city council holds office only until the date of a special election which shall immediately be called to fill the remainder of the term. The special election may be held on the date of the next regularly established election or regularly scheduled municipal election to be held throughout the city not less than 114 days from the call of the special election. (d) (1) Notwithstanding subdivision (b) and Section 34902, an appointment shall not be made to fill a vacancy on a city council if the appointment would result in a majority of the members serving on the council having been appointed. The vacancy shall be filled in the manner provided by this subdivision. (2) The city council may call an election to fill the vacancy, to be held on the next regularly established election date not less than 114 days after the call. (3) If the city council does not call an election pursuant to paragraph (2), the vacancy shall be filled at the next regularly established election date. (e) (1) If the city council of a city that elects city council members by or from districts elects to fill a vacancy on the city council by appointment as a result of a city council member resigning from office, the resigning city council member may cast a vote on the appointment if the resignation will go into effect upon the appointment of a successor. A city council member shall not cast a vote for a family member or any other person with whom the city council member has a relationship that may create a potential conflict of interest. (2) If a city council member elects to cast a vote under this subdivision, the city council member shall be prohibited from the following actions for a period of two years after the appointment of a successor: (A) Advocating on any measure or issue coming before the city council in which the city council member may have a personal benefit. (B) Entering into a contract of any kind with the city or a city vendor. (C) Accepting a position of employment with the city or a city vendor. (D) Applying for a permit that is subject to the approval of the city council. (3) This subdivision shall not apply to any city council member who is resigning from the city council due to charges of, or conviction for, corruption or criminal behavior, or who is subject to a recall election.