Hey Aisha. I just looked up some information for you about Clark Park. You can have a picnic BBQ there without a permit but if you have 50 or more people there for a party you probably will need a permit. Also I would make sure you check and make sure that they're not having a event at Clark's Park. I hope everything work out for you.
I have seen people carry use and throw grills for bbq in the park. I think it is free.
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