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From a fellow GA resident, the answer is YES you do.
As a GA resident, you are required to file a Georgia income tax return if any of the following apply:
(a) You are required to file a Federal income tax return;
(b) You have income subject to Georgia income tax but not subject to federal income tax; or
(c) Your income exceeds Georgia’s standard deduction and personal exemptions.
These requirements apply as long as your legal residence is Georgia even if you are temporarily absent from the state or live outside the state temporarily. Even though your income may be less than the filing requirements (personal exemption(s) plus standard deduction), you may file a return to receive a refund of tax withheld.
GA will allow for a tax credit on the tax NY applies to you as a nonresident performing services in NY.
Please remember that you are required to rate in a positive way (look for the STARS or SMILEY FACES) so I am credited with responding.