This year we have seen a number of states issue 1099-G and other forms that have tax withheld in box 11, but boxes 10a and/or 10b are empty. TurboTax requires that if box 11 has a value, then boxes 10a and 10b must also have entries.
Box 11 is the state tax withheld. If no state tax is withheld, you don't need to enter anything for boxes 10a, 10b, or 11.
Box 10a is probably the two-letter state code for your state (example: "MI" for Michigan). The filer identification number for box 10b is likely to be the same to the Payer’s TIN on the left side of the form.
Is there a Payer's TIN (like an EIN) on the letter?