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You can use Semi auto,, just no more than 5 rounds in the magazine.
I've got a Ruger mini 30 (7.62x39mm)for my boys, law man wont appreciate the 30 round mag.. but then again, if you cant down the deer in two shots,, then practice is needed! hah aha...

It's considered a legal gun to hunt with using the 5 round magazine.
Waterfowl shotgun, it's 3 rounds and must have plug installed
Semi auto's are fine for hunting, no more than 5 round
Handguns for big game, no less than .357 (barrel length limit drop'd as of last season - used to be minimum of 6")
No limit on muzzle load rifles, but can not hunt big game with powder pistols
I dont go for antlers, but do manage (especially this last season) to get a couple bucks.. to be honest, it's all about venison sausage, summer sausage, steaks and some amatuer jerky makin'!

Of course without sayin,, the experience and excitement of the hunt as well....
(hey Hotspot.. how's that for a rack of summer sausage!)
Here's a pic of some breakfast sausage rolls... Got me hungry thinkin about it!!