Patients who have been admitted at public expense to any institution to which this chapter is applicable may be involuntarily transferred to the proper state hospital for persons with mental illness in the manner prescribed by sections 229.6 through 229.13. The application required by section 229.6 may be filed by the administrator of the division or the administrator’s designee, or by the administrator of the institution where the patient is then being maintained or treated. If the patient was admitted to that institution involuntarily, the administrator of the division may arrange and complete the transfer, and shall report it as required of a chief medical officer under section 229.15, subsection 5. The transfer shall be made at the mental health and disability services region’s expense, and the expense recovered, as provided in section 227.7. However, transfer under this section of a patient whose expenses are payable in whole or in part by the mental health and disability services region is subject to an authorization for the transfer through the regional administrator for the patient’s county of residence.