Such improvements may be ordered by the Town Council and the cost thereof apportioned in pursuance of an agreement between the governing body and the abutting landowners, and, in the absence of such an agreement, the cost of improvements which is to be defrayed in whole or in part by such tax or assessment, may be ordered on a petition from not less than three-fourths (3/4) of the landowners to be affected thereby or by a two-thirds (2/3) vote of all the members elected to the Town Council.  Notice shall be given to the abutting landowners, notifying them when and where they may appear before the Town Council, or such committee or administrative board or other similar board of the Town which the Town Council may appoint for that purpose and to whom the matter of assessment may be referred, to be heard in favor of or against such improvements.