Sec. 2. (a) In a county having a consolidated city, the county board of finance is composed of:
(1) the county treasurer;
(2) the county auditor;
(3) the county assessor;
(4) the mayor of the consolidated city;
(5) the controller of the consolidated city; and
(6) the president of the board of school commissioners of the school city described by IC 20-25-3-1.
(b) The board has supervision of the revocation of public depositories for all public funds of the following:
(1) The county.
(2) The consolidated city.
(3) The school city.
(4) Any other political subdivision in the county whose local board of finance designates the county board of finance for those purposes.