Whenever it shall have paid or provided for the payment of all of its outstanding obligations, and it shall appear to the board of trustees of an authority that the need for such authority no longer exists, then upon petition by the board of trustees to the county board of the county in which the authority is situated, and upon the production of satisfactory evidence in support of such petition, the county board shall enter an order declaring that the need for such authority no longer exists, and approving a plan for the winding up of the business of the authority, the payment or assumption of its obligations, and the transfer of its assets.