The officers were waiting inside at the University of Chicago Medical Center when the mayor approached them and they turned their backs on her, sources said.
Chicago Mayor Lori Lightfoot is ordering teachers to return to the classroom amid an ongoing dispute between Chicago Public Schools and the Chicago Teacher's Union.
Musk has secured $ 46.5 billion (£ 35.6 billion) to fund a possible hostile bid for Twitter and is putting $ 21 billion of his money as part of the package.