Right, you don’t state it, and then hope that they don’t find out. Good luck with that.
While I’m sure a few people might have gotten away with that (and only assuming they were fairly minor issues), I’m willing to bet it is a very small minority.
I understand what sociopaths are, and acknowledge that some sociopaths have probably managed to get into the police force (and other LE positions at all govt levels), but these agencies most definitely do everything they can to weed them out.
FWIW, I think that some recruits might start with borderline personality/psychological issues, but the work can change them into full-blown problems. That is probably very likely, IMO.
If you doubt that they have some of the most thorough and invasive screening procedures (especially relative to the private sector), what else do you think they can/should do, given their resources? How would you make the screening more thorough? I’m genuinely interested in hearing your ideas.