Taxis cross state borders all the time. Probably half of Hoboken, New Jersey takes the taxi home from New York City on any given weekend night, and New York has some of the most restrictive taxi laws in the country.
Taxi licensing is mostly local, at the city or county level. A cab driver is only permitted to pick up passengers from a jurisdiction where they are licensed to do so. So, if you are in Dyer, you can almost certainly get a Dyer taxi to take you to Benton, but you may or may not be allowed to have a Benton taxi come pick you up in Dyer.
If you cross a city or county line (much less a state line), expect to cover the cost for the driver's return to his own jurisdiction in some way. A New York City taxi will charge a surcharge just for leaving New York City— and a metered rate is not possible at all for going to New Jersey; you must negotiate a flat fare with the driver (as well as pay tolls for the round trip). Washington, D.C. cabs charge a special rate for mileage beyond the District of Columbia. Since this is a rural area, you may even be required to pay the full fare of a return trip.
The taxi company will inform you of any special requirements for crossing county or state lines when you call to arrange your ride.