Your state should not have a problem with Liability coverage only; however, your finance company may not agree with it. Until you finish paying for the car, it belongs to them. Due to the car being your lien holder's asset your financing paperwork likely states that you are required to carry full coverage physical damage coverages of Collision and Comprehensive for the vehicle.
Physical damage coverages help cover the vehicle up to its actual cash value so your lien holder can recoup the value of the vehicle if it is a 'total loss' in an accident. Also if the car is damaged the car would be fixed, since a damaged vehicle is not a good asset for your lien holder either. If you do not carry Comprehensive and Collision coverages, your loan paperwork probably states that the lien holder can put forced (also known as force placed) insurance on the vehicle so that it is covered if damaged or in a total loss situation and thus protect their investment. Forced insurance would be added to your monthly car payment normally and is usually much more expensive than if you paid for your own full coverage policy. Or if you do not keep the required insurance on your car your lien holder may be able to repossess the vehicle.
If your insurance premiums are too expensive with Comprehensive and Collision coverages but your car is still financed than you should shop around to see if you can find a lower price that you can afford before dropping this coverage and end up paying for expensive force placed insurance put on by your insurer. You can click here to get an auto insurance online quote and purchase your auto insurance policy immediately.