What are the Connecticut State Laws Regarding Dirt Bike Use?

Hello, I live in Connecticut and was curious about the laws regarding using bikes on roads. I do not want to purchase a full blown motorcycle, but nor do I want to purchase a stupid pocket bike or scooter. I was thinking about some sort of dirt bike which was "street legal." However, I am not familiar with the state laws regarding this type of thing. What type of bike is street legal but still falls into the class of vehicles to which I am referring? Would I need a special permit and does this type of vehicle need to be registered and does it require a license plate? Thanks for any help. If theres is any information thats important which I did not ask about but should know, please inform me of that. I tried searching the DMV site for information but could not find anything helpful.