It's good to think ahead of time about how you are going to seek help in various circumstances. Only ask for police if somebody needs to be violently subdued or shot, because that's what will likely happen if the cops show up. Also keep in mind that the 911 dispatcher is likely to not be very bright -- DO NOT utter "key words" that might make her conclude that violent response is needed.
If it's anything to do with an anxiety attack or other medical emergency, you need to just say to 911 "I need paramedics at [address], my XXX is in medical distress". This will put the dispatcher on her "medical" script, where she will ask you for symptoms, what medications he's on, .etc
I would also hope that police departments will realize when they are not the kind of help that is needed, and will summon paramedics if they happen to get called by mistake.