Should Kent County elect to establish 1 or more library districts within the County, the County shall levy and raise by taxation a special district library tax for the purpose of the establishment of such a library in each district, and for the maintenance and increase and support of the library such sum of money as is annually approved in a budget for such purpose by the county governing body, said budget to be adopted at the same time the annual county budget is adopted. A library district may be created and a tax raised pursuant to this subchapter to raise funds to pay the Sussex or New Castle County government a contract fee to allow residents of said Kent County district the privilege of using a library located in Sussex or New Castle Counties.