Law enforcement sources tell TMZ that the actress -- who's John Cusack's older sister, and who runs a tchotchke shop there in Chi-Town -- was issued a citation Saturday after an accident unfolded that police apparently felt Joan had caused.

We're told the ticket was for driving too fast for the conditions -- although it's unclear exactly what that means. What we do know is that the aftermath was caught on camera.

Based on this video, obtained by TMZ, you can see four young women being attended to by first responders alongside their Honda -- which definitely looks dinged up -- and Joan standing by next to her pickup truck ... looking pretty annoyed by the whole thing.

The people who shot this seem to think they know what happened ... essentially, it looks like a T-bone collision -- but, again, we don't know for certain how this went down. The cops are saying that Joan was simply trying to enter a parking space when she struck a sedan.

Chicago PD doesn't offer much more of a description beyond that. The only other observation was that there weren't any serious injuries, and that Joan was the one who got dinged, legally.