Not sure what I can do but my employer never updated my address when I moved last year. Now my old state is telling me I'm going to be charged as a full year resident.

My employer never updated my address when I moved to Indiana last year. Because of this I was charged taxes as a full year resident of Kentucky. Per HR when I first filed, I split the income up using my pay stubs based on when it was earned and filed partial residency returns with Indiana and Kentucky with that info. Indiana processed fine and I paid the taxes owed for the error. Kentucky is saying that unless I get a corrected W2 showing otherwise, I need to file an amended return as a full year Kentucky resident because that's what the W2 says I am. First off by doing this, I would have to pay them additional taxes instead of getting the refund it was showing I was owed when I originally filed for being a partial year resident which balanced out the payment of taxes owed to Indiana. Second, wouldn't that be lying to the department of revenue?  I spoke with HR  and they told me that payroll will not give me a corrected W2. It seems odd that they are telling me that I need to file/pay as a full year Kentucky resident even though I have not lived there for that time frame and all of my identification, lease, etc. shows otherwise. Even if I did do that, what happens with the money I already paid Indiana?