If, upon referendum, a majority of the eligible employees included in a referendum group which is defined in section 68-621 vote in favor of including service in positions included in such group under the state agreement, the state agency shall, within ninety days after the mailing of notice of the result of such referendum, prepare a plan for extending the benefits of Title II of the Social Security Act to such employees. Such plan shall meet the requirements of section 68-608 and shall inform the managing authority or authorities whose employees are included in such group of the provisions of such plan. Upon completion of such plan, the state agency shall apply for a modification of the state agreement to make it applicable to services performed by the employees of the state or of such political subdivision or educational institution eligible for inclusion under such agreement. The state agency may prepare such applications for modification to cover one or more such plans as it deems advisable, except that the state agency shall not delay application for such modification more than six months after the preparation of any plan as set forth in this section. The state agency may require any such managing authority to furnish any information necessary for the preparation of such plan by the state agency.