The Consolidated Personnel Bylaw may be amended in the same manner in which the Town bylaws may be amended; provided, however, that no amendment to the bylaw shall be made until it has been presented by signed petition addressed to and submitted to the Personnel Board at least 60 days prior to the commencement of Town Meeting. Upon receipt of such a written petition, the Board, after giving the petitioners, the heads of the departments and employees affected at least three days' written notice, shall hold a hearing of the parties interested to consider the proposed amendment. If the Personnel Board shall fail to act on an amendment so presented within 15 days after the hearing thereon, the Personnel Board shall be deemed to have disapproved the amendment. The petition may then be presented to the Town Meeting for consideration and action, if so desired. The Personnel Board may of its own motion after a similar hearing of or conference with the parties interested propose an amendment to the bylaw.