Candidates for other than initial appointment to the board of trustees of a hospital authority may be nominated by petitions signed by not less than twenty-five electors residing within the boundaries of the authority. Such petitions shall be filed with the board of trustees not less than forty-five days prior to the date upon which the term of office of any trustee is due to expire. Not less than thirty days prior to such date of expiration the board of trustees shall cause such petitions to be filed in the office of the county clerk of the county in which the authority is situated. Upon receipt of such petitions, the county clerk shall set the date for a hearing thereon, which shall be not less than ten nor more than forty-five days from their date of filing, and cause notice thereof to be published on the same day in each of two successive weeks in one or more newspapers of general circulation throughout the area included within the authority. Such notice shall contain the date, time and place at which such hearing shall be held before the county board; the names of each person nominated for appointment to a six-year term on the board of trustees of the authority; and that at the hearing before the county board objections will be heard to the appointment of any one or more of the persons nominated. Any member of the board of trustees may be nominated for reappointment.