You might alsowant to bring water for your dog. The only water there is in puddles and the reservoir.
As Saranada said, bring waste bags. I would also suggest to check the website to see if any special events are going on. They sometimes rent the entire place out for weddings, parties and its a camping spot for the Country Fair. But best dog park by far in the area. However there are no fences, so keep that in mind if your pup is a runner.
No, just bring waste bags for your dog. There are plenty of garbage cans.
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