I had a friend who was a game warden, well experienced with deer and their proper handling. He made one mistake and it cost him dearly. He had a report of a poacher's work and went to the site. He saw what appeared to be a dead doe lying in a field. He approached it and grabbed it by a leg, to drag it to his car. The doe wasn't quite as dead as he thought and she kicked his hand with her hoof, laying open his palm. After this episode, he could no longer hold a pistol, and thus ended his career.
Always look at the eyes. If their open and glazed, they're usually dead. If they're closed, beware!