Retirement tax questions

Yes!  If the Payor is the State (for unemployment or state refund, for example) the Payer's TIN would be the same number as in Box 10b.  Box 10a would be the State Code (CA for California, for example). 

However, if you didn't have State Tax withheld (no amount in Box 11), you can leave Box 10a and b blank.

Here's more info on How to Enter a 1099-G for Unemployment or Paid Family Leave.