(a) Upon the death of a member while in service, if no duty-connected death annuity is payable, a payment of the accumulated contributions of the deceased member is payable to a beneficiary whom he has designated.
(b) Upon the death of a retired member, unless an optional benefit has been elected as provided in section 756 of this title, a lump-sum payment equal to the excess of the annual salary of the member at the date of retirement as defined in section 751(a) of this title, plus the member's total contributions, over the amounts received by the member in annuity payments up to the time of his death, must be paid to the member's designated beneficiary.
(c) The death benefit payments as provided under subsections (a) and (b) of this section is payable to a beneficiary who must be designated by the member. In the absence of a designation, the death benefit payments provided under subsections (a) and (b) of this section are payable to a beneficiary designated by the member. In the absence of a designation, the death benefit payments provided under subsections (a) and (b) of this section are payable to a beneficiary of the member in the following order of precedence:
(1) the surviving spouse;
(2) if there is no surviving spouse, to the child or children and descendants of children by representation, in equal amounts;
(3) the member's parents; and
(4) where none of the persons listed in subsection (c)(1-3) survives the member, the member's estate is entitled to receive payment of the excess of the member's accumulated contributions over the amount of annuity payment received by the member up to the time of his death.
(d) When a member dies while in service and the deceased member was qualified for a service retirement annuity as provided by the system, the deceased member's surviving spouse is entitled to a payment of the deceased member's accumulated contributions. If there is no surviving spouse, the death benefit is payable as provided in subsections (a) or (b) of this section, whichever is applicable.