The hospital administrator of a private mental hospital may transfer a patient to another private mental hospital, or the department may transfer a patient to a private mental hospital, at no expense to the state if:
(1) the patient or the patient's guardian or next friend signs an application requesting the transfer at the patient's or applicant's expense;
(2) the hospital administrator of the private mental hospital to which the person is to be transferred agrees in writing to admit the patient and to accept responsibility for the patient as prescribed by this subtitle; and
(3) written notice of the transfer is sent to the committing court.