Yes, even if you did not have a profit after expenses, you still need to file a GA return.
I cannot see your return or account here, as this is a public forum. However, this does not sound correct. You may want to very closely double-check your data entry. You may also want to look at your forms. Here's how to look at your current-year return forms:
Thank you again Gisele for your response. I checked the 1040, and everything appears correct. The mistake seems to lie in the transfer of federal return information to state. My interest and dividends earned from a brokerage and savings account are being transferred to my non-resident state (Georgia), causing me to have to pay taxes in Georgia despite my actual profit in Georgia being <$0 (rental income - expenses = negative).
I am unable to change the quantities for Dividends and Interest Income from Georgia to my home state (they are greyed out and can't be edited). I would be happy to share my return with you in order to show you thie issues I am having.