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He has since been taken to the hospital for his injuries, but his condition has not yet been made public.
The standoff was first reported via the San Jose Police Department Twitter page Wednesday morning just after 5 a.m.
According to San Jose Police, the suspect allegedly killed two people over the last 12 hours prior to the standoff, one in San Jose and one in Modesto.
He pointed his gun at a Special Operations officer before police opened fire and also reportedly shot at officers during their pursuit. No officers were harmed during the altercation.
The standoff was at the 100 block of Bendorf Drive, according to the Twitter thread, and traffic had to be diverted during the early morning hours.
It's not yet clear who the victims were of the earlier two homicides, except that one was San Jose's 17th homicide of the year, according to police, and took place at Mt. Shasta Dr.
He then committed the second homicide in Modesto, before returning to San Jose when the standoff ensued.