The staff member had not interacted with Newsom or with staff that routinely interacts with the governor, the statement said.
Separately, a state employee who works in a space shared with some staff from the governor's office also tested positive for COVID-19 but the person also had not interacted with the governor or his close staff, the office said.
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The governor's office said it received word of both positive tests earlier this week and COVID-19 protocols for California state agencies were implemented.
"Under privacy laws, we cannot disclose the office location where these employees worked," the statement said.
Newsom said during a briefing Wednesday that he has been tested multiple times and has never been positive. He said his last test was an hour before he met with President Donald Trump on Sept. 14. "And I look forward to getting tested again," he said.
The protocols when a state employee has potentially been positive at work include deep cleaning of shared spaces and asking those who interacted with the person or shared work spaces to isolate and seek testing, the office said.
The governor's office said mask wearing is mandated, minimal staff is physically present at work, most meetings have been converted to video conferencing, and seating capacity is reduced when meetings can't be done remotely.
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