California
Penal Code PC § 4023
In the event a prisoner elects to decline treatment by the county or city jail physician and to provide medical treatment at his own expense, the sheriff or chief of police may have him removed from the county or city jail to a privately owned and operated medical facility or hospital located in the county approved by a judge of the superior court for such treatment. The prisoner shall be liable for the costs incurred by the county or city in providing the necessary custody and security of the prisoner only to the extent that such costs exceed the costs which would have been incurred by the county or city in providing such custody and security if it had provided treatment for him. The prisoner shall at all times remain in the location specified by the court and at no time be permitted to be housed or detained at any facility other than that designated.