“When cops do a traffic stop do they have access to handgun permit data?”
In California they do. The handgun is tied to you via your D/L through the DMV.
In Ohio too. If you’re driving a car registered in your name and you possess a CCW the officer will be able to find that out before he ever leaves his car when he runs the plate. Advice from the course instructors drilled into us was hands at 10:00 and 2:00 and first thing out of your mouth is to tell him you have a CCW. The couple times I have been stopped (once for a brake light out and another time for expired tags on my wife’s car) the officer seemed to appreciate it and was friendly and professional. But giving them a list of what you own in your home? ... no freaking way.