Officers responded to a report of an injury collision near California and Bay Streets around 12:30 a.m.
Arriving officers found a woman with lacerations on her face. She told police that she and a friend were confronted by a woman inside of a liquor store, police said.
The women left the store and as they headed down Younglove Avenue, they noticed the woman who had confronted them was following behind them in a car with two other people, police said.
As they continued driving, the suspect's vehicle struck their vehicle, once on the driver's side and again on the passenger's side, bringing their car to a stop, police said. The unknown woman then allegedly approached the victims and began hitting one of the victims before heading north on California Street.
Officers canvassed the area and found the suspect vehicle as well as three people matching the suspect descriptions near Mission and Trescony streets. They were identified as Santa Cruz residents Nour Daniel, 23; Mauricio Perez, 27; and John Dively, 36.
All three were booked into Santa Cruz County jail.
The victim suffered minor injuries but refused medical treatment, according to police.