Money payments and special services under the adoption subsidy program shall be funded by: appropriations to a local department for the maintenance of children in foster care; and money that is made available to a local department from other sources. Medical assistance and medical care under the adoption subsidy program shall be funded by: savings for the fiscal year by the Maryland Department of Health and the Department of Human Services that are attributable to adoptions under this subtitle; and appropriations to the Department of Human Services for the adoption subsidy program. The Administration may reimburse the Maryland Department of Health for the cost of medical assistance and medical care directly or through a contract with the Department.