Once you cover your car, you have an "expectation of privacy", they either need your permission or a search warrant to look under it. If they do it without either and try to cite you or tow the vehicle, then that falls under another category...illegal search and seizure.
Former neighbor in Mesa AZ had a car backed in his driveway under a cover. It did not stop the code enforcer from walking up his driveway and lifting the cover to verify the tabs were current. Don't know if it was legal or not.....