The district attorney's office said there was no specific victim when Officer Phillip White made the controversial tweets following threats he had received on his voice mail.
One tweet said, "Threaten me or my family, and I will use my God given and law appointed right and duty to kill you."
Another said, "By the way, if anyone feels they can't breathe or their lives matter, I'll be at the movies tonight, off duty, carrying my gun."
The second tweet referred to grand juries in Missouri and New York, deciding not to indict police after officer-involved shootings.
"The police were unable to find any person who could say they were in sustained fear for their safety, so therefore there's no victim," said Deputy District Attorney Luis Ramos.
A coalition of community groups marched last month, carrying petitions with 15,000 signatures, seeking criminal charges against Officer White. District Attorney Jeff Rosen and San Jose Police Chief Larry Esquivel were on hand to meet with them. They say the matter is not over.
"There is no way to move forward to positive community police relations as long as Officer White is allowed to be a police officer. That is not a fork in the road moment for San Jose. That's an either/or type moment for San Jose," said Raj Jayadev of Silicon Valley De-Bug.
Because a member of the public filed a complaint against Officer White, an internal investigation is now underway, which by law can take up to 365 days to complete.