Whenever under the provisions of the general statutes or any special act, any action for a vote by the electors or voters of a municipality is to be initiated by the petition of such electors or voters, in addition to such other requirements as such statute or special act may impose, such petition shall be on a form prescribed or approved by the clerk of such municipality, and each page of such petition shall contain a statement, signed under penalties of false statement, by the person who circulated the same, setting forth such circulator’s name and address, and stating that each person whose name appears on said page signed the same in person in the presence of such circulator, that the circulator either knows each such signer or that the signer satisfactorily identified himself to the circulator and that all the signatures on said page were obtained not earlier than six months prior to the filing of said petition. Any page of a petition which does not contain such a statement by the circulator shall be invalid. Any circulator who makes a false statement in the statement hereinbefore provided shall be subject to the penalty provided for false statement.