With respect to the employees of any city or town or agency of the state included in § 36-7-2(1)(iii) which has elected to participate in accordance with and pursuant to § 36-7-6 and § 36-7-7, which employees are members of a retirement system, the legislative body of the city or town or agency may request the governor to authorize a referendum to be conducted pursuant to § 218(d)(3) of the federal Social Security Act, 42 U.S.C. § 418(d)(3), as amended, on the question of whether service in positions covered by the retirement system shall be excluded from or included under an agreement under this chapter.