Quick search by citation:

22 U.S. Code § 4086 - Entitlement to vote in a State in a Federal election; preconditions; applicability

(a) Except as provided in subsection (b) and in such manner as shall be otherwise authorized by a State or other jurisdiction within the territory of the United States, a member of the Service residing outside the United States shall, in addition to any entitlement to vote in a State in a Federal election under section 3 of the Overseas Citizens Voting Rights Act (42 U.S.C. 1973dd–1), be entitled to vote in a Federal election in the State in which such member was last domiciled immediately before entering the Service if such member—
(1)
makes an election of that State;
(2)
notifies that State of such election and notifies any other States in which he or she is entitled to vote of such election; and
(3)
otherwise meets the requirements of such Act [42 U.S.C. 1973dd et seq.].
(b)
The provisions of subsection (a) shall apply only to an individual who becomes a member of the Service on or after November 22, 1983, and shall not apply to an individual who registers to vote in a State in which he is entitled to vote under section 3 of Overseas Citizens Voting Rights Act [42 U.S.C. 1973dd–1].
Editorial Notes
References in Text

The Overseas Citizens Voting Rights Act, referred to in text, probably means the Overseas Citizens Voting Rights Act of 1975, Pub. L. 94–203, Jan. 2, 1976, 89 Stat. 1142, which was classified generally to subchapter I–E (§ 1973dd et seq.) of chapter 20 of Title 42, The Public Health and Welfare, and which was repealed by Pub. L. 99–410, title II, § 203, Aug. 28, 1986, 100 Stat. 930.