If you actually had an amount in box 11, then state taxes were withheld on the income that the 1099-G is reporting. In this case, you need to enter something in box 10b as well as the data in 10a.
In box 10a, enter the abbreviated name of the state. In box 10b, enter the filer's state identification number. The state number is the filer's identification number assigned by the individual state.
You will need to contact the issuer of the 1099-G for the correct value to put into box 10b. It may be the same as that entity's EIN (Employer Identification Number), but it could be different as well.
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