In a city subject to this act, and in which the board of public works has been abolished as provided in this chapter, the council, on petition to them of 100 registered electors of the city praying for the re-establishment of the board of public works in the city, shall, by resolution, submit to the qualified electors of the city at the city election held in the month of April next following the proposition to re-establish the board of public works. If 2/3 of the electors voting on the proposition vote in favor of the board of public works, then the board of public works is re-established in the city and shall be constituted and selected in the same way and have the same qualifications, powers, and duties provided for boards of public works in the act of which this act is amendatory.