YES they can. The officer of the law can just claim he saw you doing it a week ago and you ran away from the scene. But also look into the possibility of someone that does not like you calling and faking a claim that your car was drifting in a parking lot. Trust me it has happened to me before and I beat it.
Find out Where And When the incident took place. It might have been that day or a week earlier.Get some video recordings from the surrounding businesses. In my experience they(managers,owners) were quite helpful. No judge in the world is going to believe a 20ish year old man driving a “tuner”/“street racing” car was doing nothing. You need a lot of evidence and some witnesses. If you were truly in the wrong the just make a plea bargain with them.