Do all states require some kind of liability insurance?

No. Some states, while not mandating auto insurance, have "financial responsibility laws" that require all drivers to be able to pay for any damage or injury they may cause. However, carrying liability insurance is still the best way for you to meet your state's financial responsibility requirements.

UM and UIM policies are offered by law in all states, including no-fault states. In fact, some states require all motorists to carry this coverage in order to gain protection from inadequate insurance coverage of other drivers.