According to the Federal Trade Commission, there is no "cooling off" period for new or used car purchases. You haven't actually purchased a vehicle until a lender and state motor vehicle department receive your signed paperwork and you've taken possession of the vehicle. If you've taken possession of the car you purchased, you must return your vehicle before the dealer sends off your loan contracts, cashes your check or submits your motor vehicle paperwork.
TL;DR (Too Long; Didn't Read)
There is no set amount of time to cancel a new car purchase, however, the sooner you do so the better. Once your state's motor vehicle department has received your paperwork, and you have possession of the vehicle, cancelling becomes more difficult.
Talk to Your Dealer
Call your dealer as soon as possible (preferably, the same or next day after your purchase) and ask to speak to the sales or general manager. If you haven't yet taken possession of the vehicle, tell the dealer you don't want to purchase the car and to cancel the sale. If you took the vehicle and completed paperwork, bring the car back to the dealer the same or next day, even if the manager tells you otherwise. The dealer is a go-between for lenders and the state's motor vehicle department. It doesn't immediately send out contracts or process your motor vehicle paperwork. Checks aren't usually cashed until the next day. If the dealer calls you back to pick up the vehicle, then most likely your paperwork has already been processed and you can't cancel the purchase.
If You Left a Deposit
If you've only left a deposit for a vehicle, then you haven't purchased it yet and you have no obligation to do so. Getting your deposit back might prove difficult, but you can still cancel the car sale unless your buyer's order states otherwise. If you have already taken the vehicle from the dealer, it can deduct cleaning or mileage fees from your deposit. If you didn't take the car and the dealer won't return your deposit, call your state attorney general to submit a complaint.
Dealer Return Option
Some dealerships offer their own cooling-off period. Read your purchase paperwork over or visit your dealer's website to determine if the option applies to your purchase. If so, cancel your purchase and return your car within the designated time frame. If your paperwork has already been submitted to lenders and your state motor vehicle department, expect to sign forms when you return your car. Get copies of anything you sign, in case the return causes any credit or motor vehicle issues.
Other Options To Consider
If it's too late for you cancel your purchase, you can still sell the car on your own or trade it toward another purchase. If you purchased a brand new car, you might have to wait to sell it. Once you purchase a new car and drive it off the lot, it becomes used and the car's value drops significantly. You may need to provide another down payment if you plan to trade in the car for a different vehicle. If you choose to sell the vehicle, you may need to satisfy the remainder of your loan balance, as the sales price may not be enough to cover the outstanding balance.