California Code, Government Code - GOV § 66621

(a) One Member of the Senate, appointed by the Senate Rules Committee, and one Member of the Assembly, appointed by the Speaker of the Assembly, shall meet with, and participate in the activities of, the commission to the extent that the participation is not incompatible with their respective positions as Members of the Legislature. For the purposes of this title, the Members of the Legislature, or their alternates if the alternates are Members of the Legislature, shall constitute a joint interim investigating committee on the subject of this title, and as such shall have the powers and duties imposed upon those committees by the Joint Rules of the Senate and Assembly.

(b) The Member of the Senate and the Member of the Assembly may appoint any person as an alternate for the member whom the member deems qualified.