No, you cannot sue your employer because of the actions of a police officer. You are partially (if not mostly) to blame for what happened. There was no need to be snappy or sarcastic. All you had to do was show your ID and explain what was going on. That would have been the end of it. By being uncooperative, you caused the officer to believe that you were trying to hide wrongdoing. Tes, the cop was unprofessional as well, but that does not excuse your behavior.
If you feel you must do something, call the police department's internal affairs unit and file a disciplinary complaint.Ask a similar question