In the event of the annexation to a park district of territory located in a county other than the county in which such district was created, the budget commissioners of the county in which such annexed territory is located shall exercise, with reference to such annexed territory, the powers conferred upon budget commissioners by section 1545.20 of the Revised Code, and the county auditor and county treasurer of the county in which such annexed territory is located shall exercise, with reference to taxes levied and collected by the board of park commissioners upon such annexed territory, the powers conferred upon auditors and treasurers by section 1545.22 of the Revised Code.