If it's going to be a significant large group of people, I'd recommend you make a reservation for a picnic area. They are all named and you can reserve picnic grove by name. You can reserve it by going to the union county website park reservation link.
you can do it you do not need permission just arrive early to be able to take one of the places they have to do BBQ
If you have your own grill, you can take it and put it at the grilling and picnic areas. There are tables too all around the park.
I believe that that you need permission to grill. Ask for it early because the spots are taken quickly. Or you can find a spot and set up there but you can't have a large group for that.
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