No - You would only need to file a GA state return if you want a refund of any GA withholdings. Otherwise no GA state income tax return is required (since you did not actually live in GA at all during the 2017 calendar tax year.)
In
order to get the full refund of your GA state income tax withholdings, you will
need to file a nonresident GA return but report zero "0" income from
GA. You
must mail in this GA nonresident state income tax return and include your state
W-2 information. You will want to include an explanatory statement with your GA
return stating your situation (that your employer withheld GA taxes from
your wages in error due and that you were not a resident of GA for the entire 2017 calendar tax year.)
