It depends. If you are a spouse not covered by MSRRA (you aren't able to claim the same SLR as your active-duty spouse), then, yes, any money earned in Kentucky will be taxable in Kentucky. Your spouse's active-duty income will not be taxable. However, if you share the same SLR as your spouse and it is not KY, then you would pay tax to your SLR and not KY. Finally if you are both KY residents stationed in KY, your spouse's income is not taxed (KY does not tax active duty), but income that is not active duty (earned by either spouse) is taxable in KY.
For additional information, please see this FAQ on the MSRRA: https://ttlc.intuit.com/replies/3302300
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