Joe Jonas, Sophie Turner's Hit & Run Driver Can't Be Charged for Killing Dog

Joe Jonas and Sophie Turner aren't going to find justice for the hit and run death of their dog in a criminal case -- they'll have to take it up in civil court if they want retribution.

Law enforcement sources tell TMZ ... the driver who struck and killed the couple's Alaskan Klee Kai, Waldo, did not stop or leave any information when they hit the pup earlier last week in NYC. We're told they left the scene, but it's not a crime to do so.

Our sources say that the driver cannot be criminally charged with Waldo's death because the dog is considered property, and the incident is viewed as an accident.

As for why the driver didn't stop -- it's unclear for now, but we're told it is not uncommon for NYC drivers to be unaware that they've hit something, let alone an animal, and keep going. The hustle and bustle of a big city oftentimes allows for such situations.

Keep this in mind too ... the dog got away from its handler and darted into the street, where it was hit. Our sources say there was no intent from the driver to kill the dog.

When it comes to the report that Joe and Sophie filed with the police a couple days later -- our sources tell us it was NOT a criminal report, simply an accident report ... which falls under the purview of the New York State Department of Motor Vehicles.

That, of course, means that if they wanted to pursue a claim against the driver -- whom we're told has not been identified yet as the investigation continues -- Joe and Sophie would have to sue the person and take them to civil court ... possibly for the cost of the dog, emotional distress or anything else they could legally justify in that setting.

As we reported ... Sophie and Joe have been very distraught since the death of their pooch, which has left the "Game of Thrones" actress literally clutching to its brother, Porky.