If you want to hold your skateboarding competition on a privately owned skatepark or on private land, then you'll have to ask permission there, too. But, that should be a little easier.
Now, there is a third option for a place to hold your contest - some abandoned place, a huge concrete slab somewhere, a drainage ditch - some cities have a lot of places like this. If you want to, you can pull together a skateboarding competition at a place like this, but it is very risky. Not only because the city might shut you down, but also because there's no way you are going to get insurance for something like this. Which of course means the whole contest will be a lot cheaper to run, but you can get in a lot of trouble with the city, and if someone gets hurt.
