The director of developmental disabilities may enter into an agreement with a county board of developmental disabilities under which the department of developmental disabilities is to pay the nonfederal share of medicaid expenditures for one or more of the home and community-based services that the county board would, if not for the agreement, be required by section 5126.0510 of the Revised Code to pay. The agreement shall specify which home and community-based services the agreement covers. The department shall pay the nonfederal share of medicaid expenditures for the home and community-based services that the agreement covers as long as the agreement is in effect.