Sure, you can sue if you live in a different state; however, the lawsuit must be filed in the county where the defendant (i.e., the business) resides and not through your own county court.
Often filing can be done online, although you'd need to travel to the defendents county for the actual hearing.
Make sure that the amount you are asking for in the lawsuit does not exceed the amount allowed in Small Claims for that particular state.
Gail