If you have not committed a crime in the state you live in, then no you can't be charged twice of the same offense. That would be double jepordy, and is against the law. Your home state CAN hold you until the state you committed the crime in either extradites you or drops the charges
Added: The above answer seems unclear.
If you committed a crime in state "A" and then committed the same crime in state "B" then BOTH states can charge you seperately, because you committed a separate crime in each state.
If you committed a crime only in state "A" but then fled to state "B," state "B" cannot try you for a crime you committed in another state. HOWEVER they can hold you in jail until state "A" comes for you to return you to state "A" for prosecution .