State and Military jurisdiction is often concurrent, and in fact a military rape could be prosecuted by the state, and if the military believed that the state court process did not achieve the goals of the military they could court martial. Most of the time the agencies work out a single prosecution.
Non-exclusive jurisdiction: Offenses that violate both the UCMJ and other state, Federal, or foreign laws are offenses that are subject to prosecution under the UCMJ and another legal authority. For example, if an active duty servicemember is suspected of a murder that occurs off-base in a small Texas town, both the State of Texas and the military would have jurisdiction to prosecute the murder. The determination regarding who will prosecute is usually made by the agencies involved, with the military coordinating with off-base authorities. Note: jurisdiction under the UCMJ for offenses such as the Texas murder mentioned above formerly depended upon a military connection to the offense. The U.S. Supreme Court changed this standard in the 1980s case, Solario v. United States, 483 U.S. 435 (1987). Now, any offense under the UCMJ may be prosecuted as long as the military member was subject to the UCMJ, regardless of the service-connection of the offense.
Double Jeopardy: Using the example of the small town Texas murder above, it would not be double jeopardy if the military prosecuted the servicemember under the UCMJ murder even after Texas prosecuted the the individual for murder. This is because of the “separate sovereigns doctrine,” which allows for states and the Federal government to prosecute the same person twice for the same offense. As a matter of policy, this usually does not happen, creating an extra layer of protection, a regulatory double jeopardy that is more protective than the constitutional double jeopardy. Going back to the murder example, if the state of Texas prosecuted the alleged murderer, the Air Force (for example) could prosecute the same individual, but only if the Secretary of the Air Force approves the military prosecution after determining that the civilian prosecution has failed to meet the ends of good order and discipline in the military.