Yes, if someone committed a crime that crossed the boarder between two states, it is possible for that person to be charged in each state for the same crime. 

In the United States, each state is treated as a sovereign, meaning that South Carolina is separate from another state like Georgia or North Carolina.  So, if someone commits a crime in Georgia and South Carolina, each state has jurisdiction to prosecute the criminal.  Typically, what would happen is that one state would arrest the criminal and bring him/her to trial.  After the criminal was released, the other state could then take the criminal to trial. 

The U.S. Constitution provides for protection against "double jeopardy" (being tried twice for the same crime).  However, because it is not the same entity that is prosecuting the criminal in the second trial, it is not double jeopardy that is protected against by the Constitution. 

This also happens between State governments and the Federal government because the Federal government is also a sovereign.  If a person is found not guilty in a Federal Court, the State government might then arrest the person and bring them to trial.