When any person supported or cared for by the state (1) under a program of cash assistance or medical assistance, (2) in an institution maintained by the Department of Developmental Services or Department of Mental Health and Addiction Services, (3) when an inmate of the Department of Correction, or (4) as a child committed to the Commissioner of Social Services or Commissioner of Children and Families dies, leaving only personal estate, including personal assets owing and due the estate after death, not exceeding the aggregate value, as described in § 45a-273, the Commissioner of Administrative Services or the commissioner’s authorized representative shall, upon completing a financial accounting of the estate’s assets and debt, make a reasonable effort to inform the next of kin of the decedent in writing that the commissioner or the commissioner’s designee intends to become the legal representative of the estate for the purpose of securing partial or full reimbursement of the claim of the state for care or assistance rendered to the decedent required to be recovered under federal law or the provisions of § 17b-93 or 18-85c. The commissioner, or the commissioner’s designee, not later than thirty days after making a reasonable effort to contact the next of kin of the decedent, shall file with the Probate Court having jurisdiction of such estate a certificate that the total estate is under the aggregate value, as described in § 45a-273, and the claim of the state, together with the expense of last illness not exceeding three hundred seventy-five dollars and funeral and burial expenses in accordance with sections 17b-84 and 17b-131, equals or exceeds the amount of such estate. The Commissioner of Administrative Services shall be issued a certificate by said court that the commissioner is the legal representative of such estate only for the following purpose. The commissioner shall have authority to claim such estate, the commissioner’s receipt for the same to be a valid discharge of the liability of any person turning over the same, and to settle the same by payment of the expense of last illness not exceeding three hundred seventy-five dollars, expense of funeral and burial in accordance with sections 17b-84 and 17b-131 and the remainder as partial or full reimbursement of the claim of the state only for amounts due under the provisions of federal law or § 17b-93 or 18-85c. The commissioner shall file with the Probate Court a statement of the settlement of such estate as herein provided. As used in this section, “cash assistance” means payments made to a beneficiary of the aid to families with dependent children program, the state-administered general assistance program, the state supplement program or the temporary family assistance program.