I told the trooper that I had a carry permit, and he immediately replied that he didn't care and started to continue with his investigation of the crash.
Before he could go any farther, I said "No, IT is not on me, IT is in my car." (while pointing at my demolished car). The guy that hit me, along with the driver of the other vehicle that he hit, were clearly going to the hospital (they had both rolled), and two separate sets of firemen (with at least one of them having an EMT) had already come by to check me and my daughter, so I was worried about pulling a gun out of my car with that many people around.
The trooper looked at my car, then said "Do what you gotta do.", before he walked back toward the other cars. I dug a spare IWB holster out of the glovebox, then pulled the pistol out of the holster I had clipped to the bottom of the driver's seat. While I had my pants unfastened to put the holster on, the trooper came walking back up to me with a few more questions. He continued as if nothing unusual was going on, as I finished 'what I had to do'. Never asked to see my permit, just my driver's license for his accident report.
ETA: Nashville police may have a completely different reaction.