After said hearing the board of park and recreation commissioners shall have jurisdiction to overrule protests and proceed with any such improvement initiated by petition or resolution: PROVIDED, That the jurisdiction of the board to proceed with any improvement initiated by resolution shall be divested by a protest filed with the secretary of the board prior to said public hearing for the improvement signed by the owners of the property within the proposed local improvement district which is subject to sixty percent or more of the cost of the improvement as shown and determined by the preliminary estimates and assessment roll of the proposed improvement district.