The articles of incorporation or bylaws may provide that upon demand of two-fifths of all the directors, any matter that has been approved or passed by the board must be referred to the members for their approval before it becomes effective. No referendum shall be allowed unless it is demanded by the required number of directors at the meeting at which the matter in question is adopted. The referendum of the members may be conducted by mail ballots or by their vote taken at the next annual meeting or at a special meeting called for such purpose. Immediately upon receipt of a written petition signed by at least twenty per centum of the members, the board of directors shall require the secretary to conduct a referendum on the matter set forth in said petition.