State laws differ but typically you must just have proof of insurance, your insurance card normally, available to be shown upon request by law enforcement, the DMV and other state entities. Also if you were in an accident than you and the other driver should show your insurance cards when trading information.
For example the California Department of Motor Vehicles (DMV) notes that since 2006, all insurance companies are required to report insurance status information to DMV for all private use vehicles (CA Vehicle Code 16058) and law enforcement and court personnel have access to DMV records to verify that your California registered vehicle is currently insured (CVC 16058.1).The CA DMV though specifically and emphatically states that even with these laws in place one must still carry proof of insurance in their vehicle at all times.
The New York Department of Motor Vehicles also notes that one should keep an insurance card with the vehicle. If a police officer requests your proof of insurance, you must show your Insurance Identification Card in NYS.
Even if your specific state's statutes and law do not expressly say that the insurance card must be in a vehicle with a person while they are driving, it is always advisable to carry the car's insurance card with the vehicle in case a law enforcement officer requests proof of insurance or if you must provide this insurance information to others after being in an accident.
As long as you have proof of insurance to show when requested it normally does not matter if you keep it in your wallet or in the car itself. If you loan out your car to others it would make sense to keep the insurance card in your vehicle so that the driver borrowing your car has proof if they need to show it to law enforcement. Also there is the chance that you could leave your house without your wallet or have your wallet stolen and just happen to need to show your insurance and be unable to do so. Failure to show proof of insurance can end up with you paying fines or at least the hassle of going to court to show that you did have insurance in effect on the day of the traffic stop or accident.
Some insurance companies provide you with 2 insurance identification cards for your vehicle. This way you can carry one on you personally, in your wallet, while the other one stays with the vehicle.
You can contact your state's DMV or insurance regulator for them to advise you on your state's laws regarding carrying proof of insurance (an insurance identification card).If you want to shop around discount auto insurance.