central Mississippi. The  Mississippi River forms the western border for most of that state.  If Harvey Oberst (the fugitive being chased early in the film) made  it as far as a bridge to Arkansas, he would have been at least 100  miles out of the jurisdiction of the Sparta police (who catch him).  Even if, unbeknownst to the audience, the Sparta police had been  deputized by some other jurisdiction, it doubtful that they could  have brought him back to the Sparta jail in the time frame  presented.