SpaceX CEO Elon Musk denied the sexual assault claim and called the story a "politically motivated hit piece."
Some 5,000 Starlink terminals, which are designed to provide high-speed broadband internet, have been delivered to aid Ukraine in its ongoing conflict with Russia.
The four crew members will have 10 days to conduct research at the International Space Station.
A former decorated NASA astronaut and an international crew of paying customers will become the first to dock at the International Space Station as an all-private mission flying in SpaceX's Crew Dragon spacecraft next month.
Billionaire Jared Isaacman announced plans for three more private SpaceX flights, including the first crewed launch of Starship.