Police identified Natalie Rupnow - who also used the name Samantha - as the shooter late on Monday. A law enforcement source told CNN Rupnow "had been dealing with problems and expressed some of those in writings", which they were now reviewing.
Rupnow was a pupil at Abundant Life, a Christian private school. Her motive remains unclear. A manifesto, which has not been confirmed as genuine by authorities, was published on social media.
"A document about this shooting is circulating at this time on social media, but we have not verified its authenticity," the Madison police chief, Shon Barnes, said at a news conference. "At this time, we're still working on a motive, trying to determine why this happened."
Police said Rupnow's family were cooperating with their investigation into the killings at Abundant Life, which occurred at about 11am local time on Monday.
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