The same persons and estates as are legally liable for support of patients in state humane institutions shall be liable for support of patients in said center, in accordance with ability to pay, and the Commissioner of Administrative Services shall make the determination of such ability, in accordance with section 4a-12 and subsection (b) of section 17-295 except that, in the case of any patient who receives inpatient or day-hospital care and treatment in the research facility of the Connecticut Mental Health Center, where the primary purpose of such care and treatment is participation in a research protocol approved through established review mechanisms, as defined in memoranda of agreement and contracts between the state and Yale University, the provisions of said sections 4a-12 and 17b-223 which establish the liability of such persons and estates shall not apply.