I was just there and yes, there is ample parking in the picnic/day use area, which likely serves as overflow parking for the campground. All WI state parks require a pass but it couldn't hurt to contact the park (which may mean calling Governor Dodge) to check on overnight parking. I just posted a photo of the park map.
This is a very small park with camping sites just next to parking lot. I am not sure but with proper state park sticker that should not be a problem.
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