It will depend upon your state's laws, but in most states, if your car is registered then you will need to keep auto insurance or some other type of financial responsibility on it. Also if you have a lien holder on your vehicle (due to owing on a loan or lease) then they will require you normally not only to have the state minimum liability coverages, but also physical damage coverages of collision and comprehensive.
Most states require all motor vehicles to registered and while a car is registered for it to have auto insurance on it however some states allow you to get a special status on a car if it is not going to be driven. So if the car is inoperable you may be able to get special status on it from the DMV, you would have to check with your local state Department of Motor Vehicles though to find out what your state's laws allow.
For example, California has guidelines for inoperable cars. California law requires motor vehicles to have current registration if they are driven, towed, stored, parked on public roads or highways or parked in an off-street public parking facility at any time during the registration period.
If you have an inoperable vehicle in CA and it will not be in any of the places listed above, you can apply for non-operational status on the vehicle and pay a planned non-operation (PNO) fee. Once this status is placed on a vehicle's record, it remains until you decide to operate the vehicle and pay full registration renewal fees.
Another example is in Connecticut. In the state of Connecticut if you do not want to pay insurance on a car that is inoperable or being stored you must turn in your plates to the DMV and request that they be put on "hold." At that time, you may drop insurance coverage on the vehicle. When you are going to once again drive the car you would need to inform the CT DMV and get insurance on the car.
Check with your state's Department of Motor Vehicles to find out what state laws allow for in your situation. Do not take off insurance without contacting your DMV and likely turning in your registration and plates. If you do take off insurance without turning in your plates and registration then many states will cite you and penalize you for a lapse in insurance.
For example in South Carolina if your liability insurance is cancelled or expired, you must return your vehicle's license plate and registration to DMV or reinstate your coverage. Otherwise, your driver license and vehicle plate will be suspended and you will be subject to a reinstatement fee of $200 and $5 penalty for each day the vehicle was uninsured or plate(s) was not turned in. The maximum penalty for the first offense is $400 per vehicle.
If you do not plan to keep registration or insurance on a vehicle that you do not drive then you will also need to find out from the DMV where you can park this car. Normally you will need to have it in storage, your own garage or private driveway since unregistered and uninsured cars are not usually allowed even to be parked on public roadways.
If you determine that you must keep insurance on a car that you do not drive, find out how to get the best car insurance here with us.