She's accused of intentionally coughing on the child at the San Jose Yogurtland last Friday in a dispute over social distancing.
The boy's mother says police have shown her a photo lineup and she's identified the woman.
VIDEO: Mother says 'racist' woman 'purposely' coughed on 1-year-old boy at San Jose Yogurtland
Thursday afternoon, district officials released an updated statement, which read in part:
"The incident that occurred at Yogurtland is despicable. There is no place in the Oak Grove School District for any employee who would deliberately cause harm to a child. If the District receives confirmation from SJPD that the individual involved in the Yogurtland incident is our employee, we will take immediate action."
Stephanie Rickard, a former prosecutor for the Santa Clara County District Attorney's Office, says the woman could now face misdemeanor battery charges for her conduct.
"There's a lot of stress going on and we're seeing behaviors that are not sort of what we would expect from people," said Rickard, who has represented individuals and corporations in both criminal and civil cases.
"We're seeing more problems from other people trying to enforce the protocol, then we are sometimes from the person who's actually failing to (follow) the protocol," she said.
VIDEO: Woman who coughed on 1-year-old in San Jose is a teacher
District officials say they've been receiving threats and damages to some of their buildings since news of the incident broke.
On Wednesday, Superintendent for the Oak Grove School District, Jose Manzo, released this statement: "We are aware of an incident allegedly involving one of our employees who was videotaped coughing on a baby at a local eatery. The employee is currently off of work and not providing any services to our District students." The statement went on to say they are cooperating with police.
Meanwhile, an online petition is circulating -- calling for the district to fire her- and remove her teaching license.
Anyone with information is asked to contact Detective Dan Bowman of the San Jose Police Department's Assaults Unit at 408-277-4161.
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