Paratroopers, when a shooting occurs in the US, the murder weapon is the strongest evidence that can be used against the accused. If the police find the gun on the accused, and ballistic tests prove that it was the murder weapon, he will be convicted. That's why Michael had to drop the gun immediately. That way, if a policeman entered the restaurant almost immediately and arrested him, he wouldn't have the gun in his possession. And fewer restaurant patrons would have seen him with the gun.