Towing Issues: Police Impound, storage fees, police claim

Question
The police claim that my car was involved in a felony. However, there is no police report filed against the accused citizen. My car was towed and taken to the sheriff's impound. Is it legal for them to take my car if there is no police report filed?

Answer
Yes they can impound the vehicle and hold it till they determine that it is either involved in the crime or not. Sometimes that can take weeks.
And if it is or contains evidence then it can be a lot longer till you get it back.

And you can also be liable for the towing and storage fees.

But then again this also depends on the City and or State laws of your area, and since you did not tell me where this is I can not help much there.