RE: whose deer is it?
Where I grew up - it was always - 1st blood with BOW - Last shot GUN.
There were never any fights - (I'd never fight over a deer anyhow!). No doubt about the real laws though - 1st one that tags it - its their deer.
I recently took the hunting safety course with my son, and they said that if it ever happens to you and you really really think its your deer - then tag it as well. One thing for sure - if you don't tag it - you don't have any right to it. Call the game warden and he'll sort it out.
Keep in mind --the warden is not going to be any kind of pleased to come out and settle a dispute - so you better berprettydarn sure that you have a case.
FH