What is your goal in doing this?
First, you may be wrong. If you are, you tell the insurer this guy might be malingering, you just robbed him of treatment. Hippocrates rides up and beats you to death with a caduceus.
If you are hoping you can go tell the guy "we can't admit you, the insurance company won't approve it," well, I hope you have tremendously good malpractice insurance. Whether the insurance company pays or not has nothing to do with your liability. They can reject, but if you are the guy that just sent the dude who commits suicide out the front door of your ED, then the plaintiff lawyers are going to crush you. And rightly so.
If you are doing it just wanting to punish him, then you're a sociopath rather than a physician. You probably AREN'T a sociopath, which is why you shouldn't do this!
Lastly, we already have enough problems with folks on the phone from the insurance companies trying to dictate the care we give the patients we see in front of us. In some situations this is reasonable, but in the psychiatric ED, as a physician, you want to be in as much control of the situation yourself as you can be. You don't want Marsha the psychology BA who is angry because she is having to take your call at 3 in the morning making decisions for you about the patient sitting across from you in the exam room.
I can understand the poetic justice that a resident in a busy psych ED could fantasize about, but that's all it is, a fantasy. Otherwise, someone could easily accuse you of negligence, and they might not even be wrong.