Assuming that you're referring to Kentucky's Family Size Tax Credit, it's possible that you meet the requirements, but won't get any benefit from the credit because it's a non-refundable credit.
A non-refundable credit is one that will offset tax that you might otherwise owe. Any amount of the credit that is not used in offsetting that tax won't be reimbursed to you as part of your refund. So, if you have no tax liability, or if your tax liability has been offset by other credits, you won't get any tax benefit.
See FAMILY SIZE TAX CREDIT in the Kentucky Individual Full Year Resident Return Packet Instructions available at Kentucky's Forms page for more information.