My first year hunting I had a similiar situation. I heard a gunshot not far away and a doe came running right at my ground blind. The deer actually hit the blind I was in and flopped to the ground with her head up 2 yards away. The original shot had hit her guts and broken the back leg. I shot the doe and went to find the orginal hunter. I found him sprinting down the other side of the field with no hunter orange on. I did not have a doe permit at the time, so I called the DNR. The agent said it was technically illegal for me to shoot an animal I did not have a tag for wounded or not. However, he said I also did the ethical thing and put a mortally wounded deer down. He gave me a road kill permit so I could still keep the meat.
If I see a woundeddeer then I will always shoot it.