It depends. Kentucky's family size tax credit is not expressed in an amount but in a percentage. If you are declaring by yourself, your family size tax credit is 40% of the amount of KY tax calculated for your income. Thus, if your KY tax were $500 on your income, you receive a credit of $200 and your total KY tax is $300. Your refund will be the amount of KY tax you have paid in minus $300.
However, if it is you and a child, your Family Size tax credit is 100%. You would not owe KY state tax and would get a refund for all that you pay in. And even if you are not claiming other children on your tax return, you may still claim children living with you for the purpose of this credit. They do have to be children that essentially qualify for earned income credit for this to be the case.
Please see the following link for more information: http://revenue.ky.gov/Forms/2016_42A740(PKT).pdf (pages 12 and 13 of document)
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