Cal. ELEC § 7206

In each county the nominee of this party for Senator or the incumbent Senator, the nominees of this party for the Assembly, and any person elected to either the Senate or Assembly at a special election to fill a vacancy in that house, and the nominee of this party for Representative in Congress, and any person elected at a special election to fill a vacancy in the House of Representatives, shall be ex officio members of this committee. If the person elected from one party at the special election for an Assembly or Senate seat, or for the House of Representatives, shall be other than the nominee of that party for the same office at the prior election, the ex officio membership of the nominee shall expire immediately upon certification by the Secretary of State of the election. Ex officio members shall be entitled to all the rights and privileges, including the right to vote, and shall have the same standing in every way as other members of this committee, except they shall not be entitled to a ballot designation of incumbent upon seeking election to this committee in the next presidential primary.