I'm sure that even in the worst of situations they would maintain some kind of cooperative agreement with local law enforcement agencies in the 5-state area.
Then they're not really free, are they? If they wanted to truly be a free nation then they would drop all connections with the US government which would mean that they would have to create their own currency, have something to trade for revenue, and have their own source of income... otherwise the entire state would turn into a sort of primitive land of ghost towns.
They denied all treaties and they're in no position to demand
aid from the US government. The generous thing would be to help but we're all old enough to know how politics work. This is actually pretty scary to me, because anyone with big guns and a lot of friends could storm the place and claim the land as their own. If the US Military retaliates then the entire country would be under US control again and the entire Lakota tribe would be wiped out.
Also, anyone who's played Shadowrun is probably getting some bad feelings right now. Next thing we'll all become awakened and turn into trolls.