ButtonRelative4160's journey

I'm currently working as a summer temp in an admin department and I'm applying for a job with the state that starts in the fall after my current position ends. I'm really excited about this opportunity because it's something I would love to do and the pay is great at $58k a year! However, the application asks if they can contact my current employer, and I'm unsure if that's a good idea. Even though my role is administrative, I have some important responsibilities, and I'm worried they might think I'm trying to leave before my contract is up. I also don't want the new job to see me as dodgy. Should I mark 'no' on that question? I've heard from others that it might be fine to do so since temp positions typically end.