The immediate answer to the question is, NO. I am not aware of any State that has laws that allow this. Some States have Lemon Laws for used cars, but I'm not familiar with anything for new cars. Some dealerships may offer a "money back" policy if you are not satisfied.
If you live in California and you sign any contract, you will be unable to return the vehicle. In a rare case, I practically begged the manager of a used car lot to unwind the deal. I told him that my wife purchased a car for me prior to my purchase of their car, but I was completely unaware of it. They finally let me out, but withheld a $40.00 documentation fee and a 2.9% credit card surcharge.
$178.00 is better than a $6000 used car that I decided that I didn't want. Also, when I purchased the car, I left it at the car lot and told them that I'll pick it up in a matter of days. I guess the unwinding of the deal helped for the simple fact that the car never left the lot and I came back the next morning. It only took me one night to think about the deal and realize that I wanted out.
The most important thing is to not let the sales person pressure you into signing anything. Don't listen to 'this car may be gone tomorrow,' 'this is as low as I can go,' 'you will not find a deal better,' etc. DON'T SIGN ANY CONTRACTS UNTIL YOU ARE COMPLETELY HAPPY WITH THE CAR! If you already have and you want out, the best advice that I can give is make up any good believable heartbreaking lie such as: Someone passed in my family and I need the money to help fund the burial expenses, etc.
Go in the office crying if you have to. It may work, but it may not. YOU WILL BE CRYING FOR REAL IF YOU ARE UNABLE TO UNWIND THE DEAL. The best time to put on an act is when a sales person is with a potential car buyer. The car lot or dealership people most likely won't show their true colors in front of potential car buyers. They'll put on an act and most likely, unwind the deal. But again, this is rare, like in my case.
I am a sales representative in British Columbia. In B.C. the buyer bis protected by the Vehicle Sales Authority, and every sales rep, and dealership must be licensed in order to sell, very similar to the real estate industry. As far as returning vehicles go, yes you do have a way out of the contract, EVEN IF YOU HAVE SIGNED. If you have taken the car however, you will most likely be given a form to sign, and waive the right. For new cars you have up to 3 day's "cool down period" to reverse the deal and only 24hrs on a lease. If you change your mind within this time line there are absolutely no penalties, no matter what the dealer tries to tell you and they can't keep a dime. Also as far as credit card deposits go they are legally NOT allowed to charge you their processing fees. If they try to and you tell them you will tell their payment processing company, the company will pull their privilege to accept credit card payment, and this they do not want. They can however add all there processing costs to the vehicle cost, but can't have it as a separate charge.
Your question implied that you took possession of the new car since you want to know if you can return it. There is no right to rescind the contract. Most dealers have no written return policies. It is up the the dealer whether to undo the deal. It is under no obligation and there are costs associated with every car sale. This type of situation would be handled on a case by case basis.
The best approach would be to arrange to speak with the manager immediately and discuss your reasons in a calm and respectful manner. They may agree in the pursuit of good customer relations and preservation of a good business reputation- depending on your reasons. You may be required to pay the dealer's costs associated with your purchase.
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