5 C.F.R. § 837.802
(a) Generally. An annuitant who has performed reemployment service after the commencing date of annuity under the provisions of another retirement system, and who is entitled to an annuity benefit from the other retirement system during a period in which he or she is also entitled to an annuity benefit under CSRS or FERS, may receive both benefits simultaneously, or for the same period, except that the annuitant may not receive both benefits simultaneously, or for the same period, if—
(b) Election of alternative benefits.
(f) Agency responsibilities. The agency responsible for administering another retirement system must—