I agree: stay calm and tell any police doing a "welfare check" that he's A) being manipulative because he knows you're planning to break up, or B) vengeful because you've broken up. That sort of manipulation is why the police won't pull you in on his word alone.
And as your boyfriend, he doesn't have the legal pull to get you committed. Pretty much no one does except parents (even of an adult child) or legal spouse --my sister tried to get me committed and she didn't have the legal right, so she tried to convince/bully my mother into it (she refused). He can send the police around, and that opens the door for them to make their own decision, but if you stay calm and have a good story, they can't pull you in without reasonable cause of suspicion. And it isn't hard to talk your way out of it if you stay cool. They had written evidence on me, when TimeCave sent the police my suicide note, but I still talked my way out of it by explaining that I'm a writer, and was corresponding with another writer about a story I was working on.
Key point: stay calm.