I'm Lucy, and I'd be happy to answer your questions today. I'm sorry to hear that this happened.
Leaving the scene of an accident where property is damaged is a Class A misdemeanor. 625 ILCS 5/11-404. If anyone at the scene of the accident saw you hit the sign and got your information, you could be charged with a crime. You are not required to contact police to turn yourself in or tell them what happened. If police contact you, you have no obligation whatsoever to talk to them, and you're allowed to bring a lawyer with you if you choose to do so. They'll ask for your insurance information, and there could be additional charges for driving without insurance. Before they can punish you for a crime, they have to give you notice of the charges and an opportunity to defend yourself, so there's plenty of time to get a lawyer if you need one. Most likely, if you don't have a criminal record, they'd ask you to pay a fine, pay to replace the sign, and maybe do some community service or serve a term of probation.
You're also legally responsible for paying to repair any damage to your father's car, even if you didn't have insurance at the time of the accident. If he actually took you to court (and I hope he wouldn't), the judge could report the accident as a hit and run after hearing how the car was damaged.
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