If you want to have funsies... Union City is located on the state border between Ohio and Indiana (Darke & Randolph Counties). It's actually two separate gubments, but it is in many ways still laid out as one city.
College Corner is a smaller town in a similar situation, but not only does it lie across the OH/IN state line, it also lies on the border between Butler and Preble counties on the Ohio side of the line. So it lies in three counties in two states!
The former high school gym sits with the half court line on the state line, so if you can make a half-court shot, you can make a basket in Ohio by taking a shot in Indiana and vice-versa.
--z