You ask about getting a permit without proof you owned it. You have to show proof you bought the cart. Then you can apply for a permit to use it-this is not a quick process. Most folks ride on the old permit till they obtain their own. You do have to get insurance. Everything takes a lot of time here. If you can not wait, try Florida.
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Life is not about waiting for the storm to pass, it's about learning to dance in the rain.