Are you entering a state refund on a 1099G?
If you filed form 1040 check if you have a Schedule A for Deductions or if you just took the Standard Deduction. If you don't have a Schedule A then you did not itemize and the refund is not taxable.
If you filed form 1040A or 1040EZ you took the standard deduction and don't have a schedule A, so the state refund is not taxable.