I am an LEO in Ohio and I honestly have no idea LOL. I do know a few of my firefighter buddies who went and got Florida CCWs within the last year or so because Florida has such a high reciprocity rate. That said, these guys also have Ohio CCWs, and I never really asked them the above question.
Someone mentioned MDT hits, and that would definitely be correct. Without really getting into specifics, I'm certain a FL CCW ID would not show up on an MDT return.
One last thing to note, Ohio is a MUST notify state. If you have a ccw and a weapon, you must notify any LEO who comes into lawful contact with you or face CCW charges. On a sidebar, like most things, cops form their own opinions on matters. In my ****ty little ghetto, I'm much less worried about valid/legal CCW permit holders than I am about everyone else there who has guns illegally. Truth be told, I wouldn't ever be there without a gun, it's not a nice area lol.
Sorry Chief I wish I could answer you better, I'll ask around tomorrow and see what I come up with.