Yes, the papers were filed in court, links have already been provided but here it is again.
Family Court Case Information - Case History
The documents shown can be requested, usually just a cost per page. LE probably has those fees waived.
This article explains a little more about her evading the 72 hour hold:
Lawyers: Charles Vallow predicted who would be responsible for his death
"The divorce papers also show Charles tried to get Lori mental health care help. Lori refused his requests to see a doctor, court documents said. She didn’t want doctors to discover she was a translated being. Charles then went on to petition Community Bridges Healthcare for a 72-hour hold and evaluation of Lori. He set up a time for her to arrive at the care center, but Lori never showed up.
“Community Bridges then informed (Charles) that based on the information he provided them, they would be issuing a 72 hour involuntary hold petition to Gilbert Police instructing the police department to take (Lori) into custody and transport her to Community Bridges if she made any contact with the police,” the document stated.
It appears Lori never did contact police and was never taken to Community Bridges.
The court documents make clear that it was not just his own safety Charles feared was at stake. Charles requested his request for temporary custody be accelerated through the court.
“Father is greatly concerned for Mother’s well-being and the minor child’s best interests. Father is worried that the child will be affected by Mother’s mental instability if Mother continues to go without seeking professional help.”
So all of the information they needed was available. They just didn't do the work. Moo