Don't know the exact law, but, it doesn't hurt! One other word of advice. When stopped by law enforcement DO NOT say the word gun, weapon, or anything close to it! The advice I received from a brother in law who is a deputy in central michigan is to put the CPL out the window on top of your license and registration.
He told me of a situation in which he was called to do a swing by for a routine traffic stop by one of his newer deputies. He was only maybe a minute behind the new guy that made the stop. As he pulled up behind the other officers car he saw the officer remove the driver from the car via the open drivers side window.
The new guy said that when he got to the guys car, he annouced that he had a gun! Before the driver could fully explain that he also had the CPL, the officers training kicked in and out he came.
Lucky for both of them that the officer didn't draw his service pistol and start shooting
. After the driver had kissed the blacktop and was wearing a new pair of cufflinks, he explained about the CPL and was helped up. He realized that maybe he should of said it in a different way.
I have been stopped a couple of times while carrying concealed. The CPL went out the window, the officer asked if I had it with me, I said yes, I asked if he wanted it, he said no thats ok, and everything went smooth. In both cases they never asked me to produce the "Green Card", but I always have it.
I don't know where you are at in Michigan, but here in the center of the state the working conditions are getting worse for the cops. They have to be a little more keyed up because of the increase of trouble they are running into.
Carrying the cards is ok with me because at least we can get the CPL now. It used to be if you weren't the best friend of the local police chief you would never get one.