My name is***** and I will be helping you with your question today. This is for informational purposes only and does not establish an attorney client relationship.
This is a very iffy situation but I think the police can very easily argue that this was in fact a traffic stop. Towing the car might have been inappropriate since it was at a family members house and see the first link below that shows when police can tow the car. I'm not sure this situation fits but the burden will be on you to make your case. It will probably be best to hire an attorney if you want to be the most successful but the links below will give you a start. Normally they can only be towed if the vehicle is abandoned or the owner arrested and the vehicle kept for safekeeping. This didn't happen in your situation. I thin you might have a decent argument that the towing should not have occurred.
If you ask, and the lot refuses to return the vehicle to you, you may need an order from the court to get it released. If the vehicle is legally subject to impoundment, the police agency that told the lot not to return it to you is responsible for the storage fees. You may still be required to pay for towing, and any storage up to the time that you asked to have the vehicle returned, but you should not be required to pay for storage beyond that time unless the vehicle was subject to impoundment. Even if your vehicle may be subject to impoundment or immobilization after conviction of the offense charged, you may be able to petition the court for release until the case is resolved. That way, you will avoid big storage fees if you are not convicted as charged. Also, the case may take longer to get to trial than the period of impoundment authorized by law for a conviction. You should file a motion for release with the court as soon as possible, because storage fees are often very high.
For research, you should start at the following below:
See link for statute for towing: http://law.onecle.com/illinois/625ilcs5/4-203.html
Link for Illinois vehicle code: http://www.ilga.gov/legislation/ilcs/ilcs3.asp?ChapterID=49&ActID=1815
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