LE acted upon the written complaint filed by Michelle ( possibly accompanied by a witness statement). In most states there are stiff penalties for filing a false report that include perjury charges.
Yep. And in these situations where the defendant isn't in the jurisdiction to arrest the proper procedure would be to turn a probable cause affidavit to the prosecutor, along with any evidence, and let the prosecutor made a decision as to whether to file charges or take it to grand jury. This was blatantly political to make such an announcement before the prosecutor has even decided to act.