Fine, charge her with lying for those 4 hours, and lets see how much more it costs taxpayers to pursue that than it did to have her sit in their substation questioning her.
Get your priorities straight.
The waste of police resources happened before her lie, when the police decided to search for her before a specified period of time had passed. At that point, she had not lied to anyone, she was acting as a free person, going on a trip.
You make a good point.
Charge the family with the expense of looking for her since they are the one's that demanded the investigation. If the family wants to take it out of her hide later then fine.
The bottom line is the taxpayers shouldn't be stuck with the bill.