While the state refund tax sounds unusual, it’s not a double taxation. Let’s say you itemized your state income taxes on your 2016 tax return but received a refund for the year in 2017 (after you filed your 2016 return).
Because you received a refund, you technically overstated your state income tax deduction on your federal return, and you paid less in federal taxes on your 2016 than you should have. As a result, your state refund could now be taxable.
That said, if you took a standard deduction last year or itemized sales tax instead of state income tax, your state income tax refund isn’t taxable.