This is J.G. Ballard's "The Insane Ones" from AMAZING STORIES January 1962. Here's my summary:
His work displays a preoccupation with psychological themes, and this is no exception: an ultraconservative world government has outlawed mental health treatment. Everybody has the right to be insane, but remains criminally responsible for conduct. The result: "psychotics loitering like stray dogs in the up-town parks, wise enough not to shop-lift or cause trouble, but a petty nuisance on the cafe terraces, knocking on hotel-rooms at all hours of the night."
Quoting a review from Galactic Journey:
Dr. Gregory, just released from prison for continuing to practice psychiatry, encounters a troubled young woman who kills herself when she can’t get any help from him. Then he finds a disturbed young man, Christian, rifling his suitcase for barbiturates to keep himself from trying to kill the leader of the government. Gregory yields and renders covert and cursory treatment—and Christian then sets off to kill the world leader, saying he is completely rational and someone has to do it. He drives off, with Gregory chasing after him, yelling "Christian, you’re insane!" This is not one of Ballard’s best: the idea is interesting but underdeveloped at this short length. But even in this minor and facile (that word again) story Ballard’s style is vivid and incisive and one hopes that he will now appear regularly in the US.