You have an automatic extension to file your Georgia return when you receive an extension to file your federal return. When you file your Georgia return, you'll need to attach a copy of your federal extension. With an extension, your Georgia return will be due October 15, 2020.
If you don't need a federal extension, you may use Georgia Form IT-303 to request an extension to file your Georgia return only. An extension to file does not extend the date for paying the tax. Tax must be paid with Form IT-560 by the statutory due date to avoid late payment penalty and interest.