Cal. Gov. Code § 6582

Upon the designation of a park sheriff in the manner provided in Section 6581, and until such time as the designation is revoked by the termination of the contract designating the park sheriff, the park sheriff shall have and shall exercise throughout the park all of the functions, duties, obligations, and responsibilities of the office of sheriff, and shall have and may exercise within the park, all of the privileges in connection with the office of sheriff, all as though the entire park were a part of the county of the park sheriff, except as to those duties constituting the civil functions of the sheriff.