I’m a certified personal Trainer and plan to do an Saturday morning exercise class. Do I have to get permission from the city?

No, you can just go grab a spot.

I would contact them just to be sure

Check with them first.

I agree with Heather..

I am sure you would be OK as long as you're not interfering with any other guests. Otherwise you'll need to get a permit from the office on Church Street across from Carver JH.

I would recommend contacting them just to prevent any issues. Good luck on your class.