Our library has a policy for long overdue materials that when a patron has $250 worth of overdue materials that are 45 or more days overdue from the original due date to turn the bill over to a law enforcement officer for delivery in person.  Then we wait. 
If your library has a policy of involving the police in such situations, could you please let me know what you do next?
Thanks,

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Cathy Carter
Benzie Shores District Library
Frankfort, MI 49635
231-352-4671
www.benzieshoreslibrary.org