There is an informal way to do it depending on the software the individual county uses.
Software like AEGIS when the Sheriff creates a permit for you, it creates a profile in AEGIS. When officers (including municipal in those counties) run your info, a profile comes up with jack diddly shit attached to it, if the county does interagency shares of records, and most do.
They know that means you have a permit.
So the true answer is, by statutory law no, but certain counties have a loophole, unintentional way of showing that someone is likely a CCW holder. It's not absolute, and if you have a record in the county then they won't guess it, but if you're a clean green lima bean, yeah, they'll know in those places.
ETA: I know Mesa and Montrose counties can tell last I knew (through this loophole) I believe Delta is interagency as well. Outside of that, I've never cared to poke which other counties have this ability.