When to tell my current boss about change?

I'm applying to my dream district today! As background, I'm changing careers through an alt-certification program. I'm currently working at a digital marketing firm in the same town as the school. My boss has a lot of clout at the school so he'd be a great reference. Problem is, I haven't told him or anyone at my company that I'm planning on leaving assuming I get a job. My question is if I apply today, when would they normally contact my references? Should I just tell him? I really want to keep this job until August (or whenever the school district starts.) Thanks!