Can a police officer run your license plate and tell if you have insurance For Michigan?

No.

Currently a police officer can run your plate through the LEIN (Law Enforcement Information Network) and get several returns. One return is from NCIC which tells if there are any national 'hits' or 'wants' for that plate (i.e. is the plate reported as stolen someplace). It also checks through a statewide file for wanted hits. One of the returns is from the SOS (Secretary of State). This return will give all of the registration information on the vehicle. Registration information includes VIN, year, make, (sometimes model) and style of the car. The SOS return also gives information as to the registered owner of the vehicle and lien-holder (bank) if any. Lastly the SOS return gives an expiration date of the plate.

By running a plate, an officer CAN also run the registered owner of the vehicle and see if they have a valid license, who they are, and if they are wanted.

Despite all that information, the officer CANNOT determine whether a vehicle is currently insured or not by running a Michigan plate.