State tax filing

Even though I received it from WV and I did not pay state taxes for it? It seems I would be required to pay them state taxes on the unemployment income since I received it from WV....not KY. Of note: on my 1099-G that I received, it does not have a state, or state tax amount (boxes 10-11 I believe). I tried putting the information on turbo tax without entering a non-resident return and it does not make me pay state taxes. I know that I owe WV the state tax for the unemployment....the only way it is calculating is if I file a non-resident WV and enter the information from the 1099-G. This then shows I owe WV but am getting a very small refund in KY. Again, I assume that is because it is crediting my home state so I'm not paying those taxes twice on the same income. Anyone have insight? I really don't want to take my taxes somewhere to get done just because I'm afraid I'm entering the unemployment wrong. I've always used turbotax!