(a) The responsibility for paying the expenses for transporting, examining, and caring for patients, which expenses are not provided for under Chapter 9 of this title, relating to the payment of costs of care of persons admitted to state institutions under the department, shall be in the following order:

(1) The patient or his estate;

(2) Persons legally obligated or legally responsible for the support of the patient;

(3) The county of the patient's legal residence, provided that the county governing authority passes an appropriate resolution assuming such responsibility; and

(4) The department, when the General Assembly appropriates funds for such purpose.

(b) The patient or those legally obligated for his support shall not be responsible for such expenses as described above when they were incurred in transporting a patient who is released by a court or a facility before involuntary treatment as not being a mentally ill person in need of involuntary treatment.

(c) The board is authorized to issue rules and regulations governing the provisions of this Code section as it relates to the department.