What state the pension originates from is NOT having income from another state. You DO NOT file Georgia state tax return.
However -
If you have Georgia state income taxes withheld from your pension income then you need to contact the pension plan administrator and have them stop withholding GA state taxes. In this case you do file a nonresident GA state tax return to get all of the taxes withheld refunded to you. On the nonresident return you enter 0 for income earned in GA.
FWIW - My pension comes from New York state and I live in Georgia. I do not file a New York state tax return.
