It's a pristine (relatively) fresh water lake ya know. Just. try your best to keep it in the same or better shape than when the you found it. One way would be to give your dog a bath before the trip, if you want to let it roll around on the beach or swim.
The day we were there we did not see any pets. I didn't see a sign no dogs allowed. But with all state parks the pets must be on a leash. I would check the state parks guidelines.
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