Cal. GOV § 9410

(a) If, in response to a question posed, or a command to produce documents or other materials issued, by the Senate, the Assembly, or a committee, a witness asserts his or her privilege against self-incrimination, and the person presiding over the proceeding directs the witness that, notwithstanding that assertion of privilege, he or she is required to answer the question or produce the documents or other materials, the witness may not refuse to testify or produce the documents or other materials on the basis of his or her privilege against self-incrimination. However, if a witness is compelled to testify or produce documents or other materials notwithstanding his or her assertion of the privilege against self-incrimination, as described in this subdivision, both of the following shall apply:

(1) The witness may not be held to answer criminally or be subject criminally to any penalty or forfeiture for any fact or act touching upon either testimony that he or she was so compelled to provide, or documents or other materials that he or she was so compelled to produce.

(2) Any testimony or documents or other materials that the witness is so compelled to provide shall not be competent evidence in any criminal proceeding against the witness except in a prosecution for perjury or contempt.

(b) In the case of a subpoena that requires a witness to produce documents or other materials but does not require the witness to personally appear, the witness under subpoena may assert his or her privilege against self-incrimination only by communicating an assertion of the privilege to the President pro Tempore of the Senate, if the subpoena was issued by the Senate, the Speaker of the Assembly, if the subpoena was issued by the Assembly, or the chair of the committee, if the subpoena was issued by a committee. The Senate, the Assembly, or committee, as the case may be, may compel the witness to produce the documents or materials notwithstanding the privilege against self-incrimination as to those documents or other materials only by (1) issuing a subsequent subpoena calling for the witness to personally appear, (2) upon that appearance, asking the witness whether he or she continues to assert the privilege, and, if so, (3) directing the witness that, notwithstanding that assertion of privilege, he or she is required to produce the documents or other materials called for by the subpoena as to which that assertion of privilege was made.

(c) Immunity is conferred upon a witness pursuant to this chapter only if the witness is compelled, as specified by this section, to testify or produce documents or other materials notwithstanding the assertion of the constitutional privilege against self-incrimination.