(a) For purposes of the Social Security Agreement, the retirement system shall be divided into two parts, known as part A and part B. Part A shall consist of the positions of state employees, other than state police, who are members but who are not covered under Social Security. Part B shall consist of the positions of state employees who are members and who are covered under Social Security, in accordance with the Social Security Agreement.

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(b) All state employees other than state police becoming members on and after October 1, 1961, shall be included under part B.

(c) The position of any part A member may, at his request, be transferred to part B, to the extent and in the manner permitted by Section 218 of the Social Security Act.

(d) The state police and employees of state-aided institutions are not covered under the Social Security Agreement and are not included under either part A or part B except as provided in section 5-158e.