Whenever a majority of the abutters in number and value upon any street or road in the thickly settled portion of any city or town shall in writing petition the city government or municipal officers of the town to improve said street or road by grading, parking, curbing, graveling, macadamizing, paving or in any other way making a permanent street of the same, or any part thereof, and to provide for the making and reconstructing of such street improvements, and such improvements are made, 2/3 of the cost thereof may be assessed on the property adjacent to and bounded on said street or road in the manner and with the same right of appeal provided in sections 3601 to 3605, which are made applicable to such assessments.