actually, if the wounded deer ran into a posted and legitimate wildlife refuge, you cannot go after it.
it is kinda dumb, but it applies to waterfowl as well, if a body of water/marsh is divided up into huntable and refuge, and you shoot a duck that falls and doesnt die, yet manages to swim over the line and then dies, you cannot retrieve it.
if an animal ends up over a refuge line, you're SOL.... unfortunate as it is, but that is the purpose of a refuge.