Actually, I'm sure of this. A "hung" jury means that no verdict was reached, and the case is dismissed without predjudice and no jeopardy is attached to the defendant.
This is not a "state's rights" issue, this is a Constitutional rights issue. It's related to the concept of "double jeopardy". No double-jeopardy exists when no verdict has been reached by a "hung" jury. A mistrial is declared, and as Dax said, , prosecutors are allowed to present the case again based on some determining factors.
In the US, the prosecutor is free to bring the same charge again, and whether that happens is dependent on the availability of witnesses, strength of evidence and estimation of likelihood to prevail, public opinion, and the cost of prosecution.
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Helice ~~~ (Nemo me impune lacesset.)
"He who joyfully marches to music in rank and file has already earned my contempt. He has been given a large brain by mistake, since for him the spinal cord would suffice."
--Albert Einstein