Global Entry members do not have to fill out the form.
CBP brochure "It's About Time", Pub # 0101-0510. "As a Global Entry member, you must declare all goods you are importing into the United States. You will be required to answer the customs declaration questions presented on the kiosk, however you will not need to complete the paper customs declaration form (CBP 6059B) before arrival."
CBP brochure "Global Entry Information Guide", Pub #0154-0513. "With Global Entry, you do not need to complete the paper Customs Declaration form 6059B before arrival." (p.4)
Both are available from the CBP website at https://www.cbp.gov/newsroom/publications/cbp-publication-catalogue. They are dated several years in the past, but are still being distributed, and I have never heard that there have been any changes in this regard.
That said, you will be asked to declare your goods at the Global Entry kiosk, and if you are over the exemptions or have anything restricted, you may be required to talk to a customs officer. If you know this is the case, it may be helpful to fill out that part of the form anyway, as a way to help remember everything you need to declare. You could also just write it down on a separate piece of paper, but having it on the official card might slightly streamline the process with the customs officer. (Thanks Zach Lipton for pointing this out.)Answer from Nate Eldredge on Stack Exchange