At any time prior to the incurring of any indebtedness or upon the full payment of all indebtedness of an improvement district, the board may by resolution set a time for a hearing on whether or not to dissolve the improvement district or a petition, signed and acknowledged by not less than the number of holders of title to land constituting the improvement district required to sign a petition to form the improvement district, may be filed with the board requesting that the improvement district be dissolved.