I had this problem between Ohio and Kentucky about 10 years ago: I moved from Ohio to Kentucky, and they both considered me living in their state for the entire year.
I gave up trying to fight it after about 5 years (!!) and just paid the $15K to the Commonwealth of Kentucky and moved on with my life.
I now live in Florida -- legally and physically -- and don't have to deal with the headache of this crazy state income tax drama.