The beach closes at 8pm and parking is free, it depends on when you go and if you are a CT resident it's free to access entrance to the park and beaches. There is camping at the state park as well.
No, you cannot park there overnight unless you are in the campground with a reservation. They close at sunset and the rangers walk the beach asking folks to leave because it's closed.
You cannot park overnight at the beach. The beach closes at dusk.... I think 8PM. If you want to stay overnight you can rent a campsite.
I think camping is $20 a night includes your car
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