Fullerton police said the incident occurred shortly before 1 p.m. at the parking structure of EvFree Church in the 2800 block of Brea Boulevard.
The second floor of the structure serves as remote parking for Cal State Fullerton students, police said. A shuttle picks students up from the parking structure and drops them off at the school's campus, authorities said.
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Responding officers found the victim, described as a 20-year-old woman, suffering from two stab wounds. She was rushed to a local trauma center and is expected to survive.
Investigators believe she did not know the suspect and that the attack was random.
"At this point in the investigation, we believe it was random," said a Fullerton police investigator at the scene. "We do not believe the suspect or the victim knew each other and we do not believe it was an attempted robbery, so we do believe it was just a random act."
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EvFree Church and nearby Beechwood Elementary School were briefly placed on lockdown as a precaution as authorities searched for the suspect. Residents were told to stay away from the area.
Around 2:45 p.m., police located and arrested the suspect, who was found hiding in a nearby neighborhood. The investigation is ongoing.
Brandon Davis, a Cal State Fullerton student and parking services officer at the university, said the parking structure is always patrolled by at least student security officers.
"We try to monitor the area and make sure it's always safe," Davis said. "So, to hear something like this, it is a little discouraging, because we do try to encourage students to come out here and park, and use the structure as much as possible."