The expenses of the removal of an adult with a criminally mental condition or a criminally inclined juvenile and of the adult's or juvenile's admission to a hospital under this subchapter, and the charges and expense for the maintenance and care at such hospital shall be paid by the institution which had charge of such case. Where such persons are committed by the proper courts otherwise than from an institution of the State, the State Treasurer shall pay such hospital for such removal, admission, maintenance and care. If any such adult with a criminally mental condition or criminally inclined juvenile has any real or personal estate, the Department of Health and Social Services or the Department of Services for Children, Youth and Their Families shall have, for the expenses and charges incurred, the same remedy as is provided in § 5019 of this title.