It happened at a mobile home community for people 55 years and older.
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The park is located in the 33000 block of Almaden Boulevard.
Union City police say they were called to the scene at 7:46 a.m. on Thursday for a report of a person stabbed.
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Once officers got there, they found three victims with injuries. One was pronounced dead at the scene, and the other two were taken to the hospital with non-life threatening injuries.
The suspect is a 21-year-old man from Mountain View.
Police say he took off in a car belonging to one of the victims, though they did not clarify how he got the car or if he had any connection to the victims.
"The suspect did not stop, and the pursuit was initiated," Sergeant Jean Jimenez with the Union City Police Department said. "The suspect began driving erratically and officers eventually lost sight of the vehicle."
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Neighbors say the community for people 55 years and up is typically quiet.
"I was actually shocked. I saw it on the news this morning," said Larry Anderson who lives nearby. "I said 'Wait a minute that's where I live,' so I went to walk over there and it was all cordoned off already."
The scene was focused around the mobile home park's clubhouse. SKY7 shots showed a black car with a door open, a bicycle in the road and a Union City Transit bus. Police said the bus had nothing to do with the investigation but would not elaborate on the car or bike's involvement.
When alerts first went out Thursday morning about the stabbing, Union City Police said that the suspect was outstanding.
INTERACTIVE: Take a look at the ABC7 Neighborhood Safety Tracker
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Later in the morning, Mountain View police confirmed that they were helping Union City police search for the suspect, who they said was armed and dangerous.
That suspect was later arrested at a Mountain View neighborhood, though police not would not confirm if he lived there.
"Our detectives are out there interviewing, exhausting all avenues, all leads just to see what the exact motive was for this incident," Jimenez said.
Union City asks anyone with any information to come forward. Information can be left anonymously at 510-675-5207 or emailed to tips@unioncity.org.