When the person proposing any initiative measure has obtained signatures of legal voters equal to or exceeding eight percent of the votes cast for the office of governor at the last regular gubernatorial election prior to the submission of the signatures for verification, or when the person or organization demanding any referendum of an act or part of an act of the legislature has obtained a number of signatures of legal voters equal to or exceeding four percent of the votes cast for the office of governor at the last regular gubernatorial election prior to the submission of the signatures for verification, the petition containing the signatures may be submitted to the secretary of state for filing.