In nearly five years of carrying with a CHP, I have only had one official contact with an LEO while I was carrying. It was a county sheriff's deputy (Saunders I believe). He stopped me for going too fast on Hwy 6 near Ashland. The road was freshly paved. I was looking for an unfamiliar road going north to Mead, and I didn't realize I was going about 60 (the normal speed limit) in a 50-mph construction zone (no workers present). He approached and asked for my license and registration, and while I was getting them out, I told him I had a CHP and was carrying. He acknowledged my statement, but didn't seem to care at all. He didn't ask to see my permit or my weapon. When I told him I was distracted because I was trying to find my way north to Mead to act as a volunteer communications operator (ham radio) for a bicycle race and didn't realize how fast I was going on the fresh, smooth pavement, he issued me a warning and told me how to get where I was going.
In my humble opinion 99% of LEOs will not hassle you in any way about a CHP (or anything else) unless they suspect you of some wrong doing, or you don't treat them with dignity and respect.