With respect to employees of the state as defined in § 36-7-2(1)(i) and (1)(ii), the retirement board, as defined in § 36-7-2(9), 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 state retirement system shall be excluded from or included under an agreement under this chapter.