Yes officers can randomly run the registration of any vehicle on any street, even a driveway as long as they can see the license plate.  Further, if there is articulable suspicion or reasonable or probable cause to believe something is going on, they can certainly run plates, look around the outside of the car but need a warrant (absent any emergencies) to search the inside of the car. If you have been arrested or issued something as a result of the running of your license plate, talk to a lawyer about the matter. If it is simply about expired tags, you may simply have to renew and pay any ticket issued as a result thereof.