Do I need to file a nonresident Georgia tax return if I did not have net income from my rental property?

[Carl]

Weather you had income or not doesn't matter. If the property was classified as "Residentail Rental Real Estate" for one single day in the tax year, then you're required to file the state return.

Note that it is "extremely" rare for rental property to ever show a taxable profit "on paper" at tax filing time. That that does not negate your requirement to report it.