Is there a 3-day cooling-off period for car purchases?

Usually not. Many people believe there is a three-day right to cancel, but the FTC's Cooling-Off Rule does not apply to cars bought at a dealer's place of business. A few states have limited exceptions, such as California's optional contract cancellation agreement on some used cars under $40,000, and some dealers offer voluntary return policies. Read the contract and ask about returns before signing, because in most cases the sale is final once you sign.