This police department screwed itself.
Sorry, but it doesn't work that way.
If an apology is warranted, issue it. Discipline the people that are responsible for this. Compensate the woman for her expenses. Drop the charges and expunge her record. Document your changes in policy to make sure this doesn't happen again.
If you do all this, then maybe she won't sue you. But, that's her decision to make, not yours.
That statement pretty much guaranteed a lawsuit...