Law or no law, you ought to have liability, "comprehensive", and collision coverage or insurance, either your own, your credit card's, or the rental company's.
As far as I know, no state requires that the renter buy or have "comp" or collision coverage.
Finance companies almost require require that cars have collision insurance, but the renter is not obliged to buy it or have it unless the rental company's rules or policies say so. The renter has no contract with, relationship with, or obligation to, the rental company's car financier until after a lawsuit favoring the latter has finished.