I think it was on the left side from the entrance of the park, there should be a way out over the wall. Before completing the story it was blocked off by a bush that shoukd be gone once you finished the story.
Then you there should be a way out. Or you could use a jump feather if you have any.
If you have slime you also just can go through the entrance gate.
Did you made it out yet?
I see, well it is not needed to get out of the park.
It can be bought in the eastern part of town.
You get in with mouse, right?
I just saw that you couldn't go back through the hole, will fix that with a patch soon.
Yup, just noticed that the mouse hole can't be used from the other side, my mistake, sorry-_-
And that the hole on the ground also can't be used to get back either.
Patch will be up soon!