Rivers are natural points for cities, almost every city not on the coast is on the river because that's how it was originally settled. So to have half the city in one state and the other half of the city in the other state is absurd. People build across anything but again cities are naturally on rivers.

Economically the immediate area on both sides of a river are going to be similar, so you should have the same administration. It's when you get away from the river that this changes and you might want different administration.