State and local laws are obviously a big varying factor here, but:

1.	If the Vehicle is Parked Legally: If you pull into a private driveway and your vehicle is parked legally, meaning it does not block traffic or pose any safety hazards, the police typically would not tow your vehicle without the property owner’s permission. However, they can still ticket you and potentially arrest you if other laws have been violated (like attempting to evade the police).
2.	If the Vehicle is Parked Illegally or is a Hazard: If your car is parked in a way that blocks the driveway, creates a traffic hazard, or if the property owner complains, the police may have grounds to tow the vehicle, possibly even without the property owner’s immediate permission.
3.	Private Property Rights: Private property owners generally have rights over what happens on their property. However, if the police believe there is an exigent circumstance or that a law has been violated that justifies towing, they might proceed with the tow and sort out the details later.
4.	Exigent Circumstances: If the police believe that your car is part of an ongoing investigation (e.g., it was used in a crime or you were attempting to flee from law enforcement), they may have the authority to tow the vehicle regardless of whether it is on private property.
5.	Local Laws: Local ordinances or state laws can vary widely on this issue, so the specific circumstances and jurisdiction will greatly affect what the police can legally do.