Golf Cart Insurance
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If you use your golf cart in places other than the golf course, which is common in retirement and resort communities, you'll need additional insurance for this sort of use. You will definitely need additional insurance if you use the golf cart on public roads.
As for whether you are currently covered on your homeowners' insurance, you will need to read the fine print on your policy. Policies differ from company to company and state to state.
Whether you need plates or not will depend on your state and how you are using the cart. Check with your state government on that.