The city or county that established the authority is authorized to make appropriations and to provide funds for the operation of the authority and to further its purposes. Such appropriations for the authority shall be subject to the requirements that are applicable to community services boards, as set forth in § 37.2-509. The Department shall allocate available state-controlled funds to behavioral health authorities for disbursement in accordance with the provisions that are applicable to community services boards, as set forth in § 37.2-509, and shall notify the governing body of the city or county that established the authority before implementing any reduction of state-controlled funds.