Wow, I don't think that CA DMV has the information regarding CC permits tied to our license plates. I've never been asked if I am carrying. "IF", MI has that info in their DMV data base, that is not cause to stop you and search you or your vehicle.
As RLS7201 posted, I think you can carry a weapon in your vehicle when stored in accordance with Federal Law. If each state could limit your activities in such a manner as to stop you from traveling interstate and enjoying your freedoms, then we would have 50 separate countries and not one country divided into 50 states. I am not a LEO, lawyer or judge, I know that it is not legal for any state to restrict your constitutional rights.