California Code, Government Code - GOV § 20320

(a) A person directly appointed by the Governor, without the nomination of any officer or board, or directly appointed by the Attorney General, Lieutenant Governor, Controller, Secretary of State, Treasurer, or Superintendent of Public Instruction exempt from civil service under Article VII of the California Constitution, except those appointed pursuant to subdivision (i) of Section 4 thereof, is excluded from membership in this system unless the person files with the board an election in writing to become a member.The election effective date shall be the start date of the current appointment, provided the election is received by this system within 90 days of the applicable start date. If the election is not received by this system within 90 days from the start date, the effective date shall be the first day of the month in which the election is received by this system.

(b) Upon electing to become a member, the person may further elect at any time prior to retirement to receive service credit for their prior, excluded state service by making the contributions as specified in Sections 21050 and 21051.