The man stopped near to the girl when she was outside Offington Park Methodist Church, in South Farm Road, Worthing, at around 11.30am on Saturday (January 10).
He got out of his car and the girl realised he had nothing on, except a long black wig, with red streaks in, which he kept taking off.
He then asked the girl if she wanted to go for a ride, at which point she ran off and called the police.
The man is described as being around 5ft 7in tall, aged around 40 to 50 and was short, fat and bald.
Police are appealing for witnesses to the incident.
Sergeant Ian Kerr said: "Obviously we urgently need to speak to this man.
"It may be that somebody recognises this as somebody's party piece, or somebody might have experienced a similar incident. We would ask them or witnesses to come forward."
Contact police on 0845 6070999.
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