Destruction of public property is no different than destruction of private property (like your own). I'd contact someone who works with the city and see what they would like you to do. They might not ask for reimbursement if its small or had prior damage.
By "hit a stop sign", I assume you actually snapped or bent the support pole. If you "turn yourself in", not only will you likely be required to pay several hundred dollars for the fix, but there is also a decent chance you will get a ticket and points for driving too fast for conditions. The law does demand that you notify the property owner of the damage you caused. If the event was not witnessed, the result of not reporting the accident would likely be 0. You decide what course of action you wish to follow.
This is from WI DMV:
When to report an accident
Any accident must be reported when it results in:
•Injury or death of a person.
•$1,000 or more total damage to property owned by any one person.
•Damages of $200 or more to government property (except motor vehicles).
Call the police immediately. They will report it for you. If they cannot file the report, you will need
To file an accident report, complete a Wisconsin Driver Report of Accident form MV4002 and mail it to:
Wisconsin Department of Transportation (WisDOT)
Accident Records Unit
P.O. Box 7919
Madison, WI 53707-7919
An accident entry will be put on the record of each driver shown on the accident report. Accident entries remain on the driver record for 4 years from the date of the accident.
Accident entries on your driver record
Regardless of fault, accidents appear on the driver record of all drivers involved in a reportable accident.
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