In a county that has an established county library, if a city council, village board, or township board of a city, village, or township that has a public library and the library board, if one exists, of the city, village, or township both adopt a resolution indicating that such city, village, or township library desires to merge with the established county library, they shall notify the county board by filing the resolutions with the county clerk. After such notification, the city, village, or township library shall be a part of the county library as provided in section 51-201.06 and its residents shall be entitled to the benefits of the county library, and the property within such city, village, or township library shall be liable to taxes levied for county library purposes. At least once a week for two successive weeks prior to adopting such resolution, the city council, village board, or township board and library board shall publish notice of such proposed resolution and the date and the place of the meeting at which such resolution is proposed to be adopted, in a newspaper designated by the council or board and published in or of general circulation in such city, village, or township.