Cold War Service Medal Act This bill authorizes the military department concerned to issue Cold War Service Medals to eligible persons who served during the Cold War (September 2, 1945, to December 26, 1991) and meet other requirements. Specifically, eligible persons are those who (1) served on active duty for at least 24 consecutive months during the Cold War, (2) were deployed as members of the armed forces outside of the United States for at least 30 days during the Cold War, (3) were members of a reserve component and called or ordered to active duty related to the Cold War, or (4) performed other service in the armed forces during the Cold War. The military department concerned may issue the medal to the next-of-kin if the eligible recipient is deceased.