A majority of the inhabitants of any village situated in two or more counties may present a petition to the county board of any county in which any part of such village is situated, requesting that they may be incorporated as a village; and such county board shall act upon the petition the same as if the village were situated wholly within the county where the petition was presented. If the county board shall declare such village incorporated, the village shall thereafter be governed by the provisions of the statutes of this state applicable to the government of villages. The county clerk of such county shall immediately certify the proceedings relating to the incorporation of such village to the county board of each other county in which any part of such village is situated, and each county board to which such proceedings shall be certified shall enter such proceedings upon its records.