No, no-fault insurance will not pay for your car repairs after an accident. Even in no-fault states, the at-fault driver is responsible for paying for vehicle repairs after an accident, as no-fault rules do not apply to property damage. No-fault states simply require drivers to use their own personal injury protection (PIP) insurance to pay for their medical expenses after a wreck.
As a result, if the other driver is at-fault in an accident that damages your car, requiring repairs, then you need to file a property damage claim through their insurance company. But if you caused the accident, then you need to file a claim with your own collision coverage.
To learn more about coverage in no-fault states, check out WalletHub's no-fault insurance guide.