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The Rosemount special education teacher has since deleted her Twitter account, but a tweet that read "so whose gonna take one for the team and kill Kavanaugh" was reported by Twitter users to the FBI and Secret Service.
The FBI in Minneapolis told The Star Tribune that it's aware of the tweet.
Intermediate School District 917 Superintendent Mark Zuzek said in a statement Tuesday that the employee has voluntarily resigned after being placed on paid administrative leave pending an investigation.
The Tribune hasn't named the woman because she hasn't been charged with a crime.
Kavanaugh was sworn in Monday after a divisive Senate confirmation hearing .
Information from: Star Tribune, http://www.startribune.com