They most certainly can if they have evidence to do so.

The standard guidance applies at this point. They may call you or even come visit you and ask you to talk to them about it. DON'T. Understand that almost anything you will say will provide evidence to your guilt even if they don't have the physical evidence. Understand that "someone asked me to hold this" is not going to get you out of anything. If you get charged or they arrest you, keep your mouth shut and get an attorney.

The good news is that a "residue" may not support a possession of drugs charge. It might indicate paraphernalia but possession of such is only an infraction in your state.