A car was flipped onto its roof and crashed into eight others before the occupants fled the scene in Hoole .
Police were called to Westminster Road after the incident at about 11.15pm on Sunday (April 10).
The three people inside the crashed vehicle had all left the area.
Officers later arrested a woman who is not believed to be the driver and their search is ongoing for another woman and a man.
A Cheshire Police spokeswoman said: "The three occupants, one man the two women, left the scene and a search was made of the area.
"A woman was later arrested on suspicion of being carried in a car taken without the owner's consent.
"Police are continuing to search for the other occupants of the vehicle."
Anyone with information should contact Cheshire Police on 101 quoting incident number 924 of April 10.
Details can be given anonymously by contacting Crimestoppers on 0800 555 111.