If you take the Standard Deduction, the state refund is not taxable.
If you itemized, but the amount was less than or equal to the Standard Deduction, the refund is not taxable.
Depending on the state you file in, you might be able to take the Standard Deduction on your Federal return and then adjust for the itemized deductions you want to claim on your state return (for California for example), but that does depend on the state.
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