Each state-operated facility for persons with psychiatric disabilities may establish psychiatric clinics and day treatment programs for adult persons, including those who are or have been committed pursuant to a Probate Court order. The Commissioner of Administrative Services shall determine financial liability for services in such psychiatric clinics and day treatment programs, and the same persons and estates as are legally liable for support of patients in state humane institutions shall be liable for payment in accordance with § 4a-12 and subsection (b) of § 17b-223.