A rider, a 32-year-old man, suffered injuries and required hospital treatment after the collision at Woodsgate Park at about 9pm on May 18.
Investigating officer PC Stuart Kenway, from the Roads Policing Unit, said: “We are appealing for witnesses to come forward.
It happened near the junction of Woodsgate Park and Buxton Road. The rider travelled south down Buxton Road, while the car travelled in Woodsgate Park in the direction of London Road.
“In particular we wish to speak to the driver of the vehicle in connection with this incident, and with two women who stopped to help the e-scooter rider at the scene.
“Information can be reported to Sussex Police online or via 101, quoting serial 1339 of 18/05.”