In case a county psychiatric hospital patient or the person legally liable for his maintenance is or becomes the owner of property, real, personal, or mixed, the county furnishing such care, treatment, or observation, shall be reimbursed therefrom for its charges. The board of supervisors of the county shall fix and determine a schedule of charges for the care, treatment, or observation of such patients, and reimbursement to the county shall be made upon the basis of the charges so fixed.