It depends. You aren't taxed on the CA refund, but you may have to use that refund to pay KY taxes. Here is what I believe is happening:
Since you are a KY resident, all of your income is taxed in KY regardless of where you earn it. It sounds like the company you are working for remotely is not withholding KY tax for you, but they are withholding CA tax. This, unfortunately, is making you file a CA return in addition to the KY return. The CA return should be a full refund: since you are not physically located in California, you are not taxed in California. There are a few states that treat the telecommuter working for a business location inside of their state as also working inside of the state, but California is not one of them.
Therefore, you will need to make sure you are filing a California nonresident return with zero income, and get the full refund of CA taxes withheld. Then, you will file the KY return. You will no doubt owe if the company did not withhold for KY. Afterwards, you will want to see if they can, so that KY tax is taken out of your check instead of CA tax. If they cannot, at least have them stop taking out CA tax, and then fill out the information in TurboTax so that you can make state estimated payments, so you do not pay penalties for not paying in enough KY tax throughout the year.
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