If it's a designated dog park, cats probably aren't allowed at all! If it's just a public park that allows pets, it's probably allowed, but I still wouldn't do it if it were my cat considering that many people allow their dogs off-leash when they shouldn't.
Just seems odd to me that they'd want to put their cats in danger like that. Maybe they've never seen a pack of dogs in action chasing a small critter.... That's why I'm not a cat owner right now. The Pack is a formidable hunting machine when the pack mentality comes over them