Nope, the sheds technically belong to the state. Edit: I will state that this was the case as of two years ago when I worked for Game Fish and Parks.
that's retarded! what's the state doing with them? nothing! kind of like new York state it is illegal to use a metal detector on beaches. dumb laws from dumb politicians once again! ask the guys that sign these laws what a deer antler shed is and I bet he has no clue.
The law is in place and worded in such a way that anything on the property in general belongs to the state. The intention is not to stop shed hunting, its just a disappointing side effect. That said not that I am advising breaking the law, but any of the COs I know would never think of citing you for it.
It's a bummer because I was trying to plan a trip out there with the wife to do some shed hunting. Glad I contacted SD GFP about it before I had everything planned. Guess we'll be going elsewhere.