Only if he left fired shells behind. It the gun was not a semi-auto, and he didn't eject the spent shell, then ballistics won't help much. Shotguns leave no identifying marks, not even enough to get the model or type of shotgun. At best they could guess the gauge by the number of pellets recovered. Even that might be problematic. Shotguns will leave firing pin and ejector/extractor marks on the expended shell, just a rifle or handgun will.
I'm almost positive that a shotgun was used.