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Your polygraph failure is noted in your FBI HQ file. I don't know precisely what information will turn up in a National Agency Check, though I suspect it might at a minimum indicate that you have a file with the FBI. That could then be requested by other agencies. To the best of my knowledge, there is no statute preventing the FBI from sharing such information with other federal agencies. I suggest that you contest the FBI's polygraph results in writing and file a Privacy Act request for all FBI records on you, including your polygraph report, charts, and related paperwork. See Chapter 5 of The Lie Behind the Lie Detector for pointers on how to procede.
I do not know whether the State Department will be concerned about your polygraph failure. By coincidence, we've just added the State Department's polygraph policy to AntiPolygraph.org. You can download it as a PDF file here:
I failed an FBI polygraph. Does it automatically go on the National Agency Check? If I try for a job with the State Department, which is vehemently opposed to polygraphs, will they be concerned if they find out about my FBI failure? I thought there was something in US code which prevented agencies from reporting polygraph results to others unless a crime was committed.