My car was towed in a Sunday, from a private parking lot, do the police have it since the place that towes for this property was closed at the time?

You need to get ahold of the towing company first normally the only cars in impound are the ones that are towed in from the police or state patrol

Look for signs at the parking lot. They should have it posted who would tow your car and have a phone number to call on the sign. Private towing company.

They have to have signs in the parking lot to be able to tow anything vehicle out of the lot. The police impound will not have it if it was in a private parking lot.