No, you do not need to file a TN return related to the capital gains on the sale of your property. The TN tax return only taxes interest and dividend income when applicable.
Since the capital gain will not be taxed by TN, there will not be a credit on your GA return for taxes paid to another state. Also, there does not appear to be an adjustment that would be made on the GA return because the gain is attributed to property in another state. This means that the full gain will be taxable on your Federal and GA return.
