Let’s see. A mobster warns that you will wind up like Paul Castellano, the crime boss who was gunned down outside a Midtown steakhouse in 1985. Maybe the guy is merely a blowhard. But maybe he is a sociopath. You’re not really sure. Either way, you’ve been handed a death threat. Shouldn’t you count on his being arrested?

What if another fellow announces that President Obama will meet the same terrible fate as did President John F. Kennedy? Maybe this guy is just running his mouth. But how do you know? Wouldn’t you expect law-enforcement agents to swoop down on him in nothing flat?

And so some people may well wonder why there have been no arrests of a few Islamist extremists in New York who announced that the creators of “South Park” would probably be murdered for their latest riff on the Prophet Muhammad.

“South Park,” the animated television series carried by the Comedy Central network, is in the business of giving offense. It is, depending on one’s sensibilities, outrageously hilarious or gratuitously tasteless. At a minimum, it pushes more buttons than an elevator operator.

Of late, the show’s creators, Trey Parker and Matt Stone, have chosen to lampoon the anger and the fear that accompany any depiction of the Prophet Muhammad, an action that many Muslims deem forbidden. Some of them have resorted to violence, as they did a few years ago after a Danish newspaper printed cartoons with the prophet’s image.

A recent “South Park” episode satirized that sort of reaction. Rather than show Muhammad — too risky, even in cartoon form — it had him hiding inside a bear costume. Only it turned out later that it wasn’t Muhammad after all. It was Santa Claus in the costume.

Behind the silliness was a serious message about intimidation and fear — a lesson apparently lost on the people who run Comedy Central. They bleeped out every “South Park” allusion to the prophet. They even bleeped out a speech on intimidation and fear that never mentioned him. They have since been widely criticized for letting their knees go wobbly.

Amid all this, a fringe radical group in the city called Revolution Muslim posted a notice on its Web site that the prophet had been insulted. Because of their “stupid” act, Messrs. Parker and Stone “will probably wind up like Theo van Gogh for airing this show,” the notice said.

“This is not a threat,” the notice continued, “but a warning of the reality of what will likely happen to them.”

Mr. van Gogh was a Dutch filmmaker murdered in Amsterdam in 2004 by a Muslim fanatic angered by a van Gogh movie about the abuse of women in some Islamic countries. Saying that the “South Park” team would end up like him sure seemed like a death threat, no matter how much Revolution Muslim denied it.

It sounded like a threat to Police Commissioner Raymond W. Kelly. That’s what he called it. So did a spokesman for the Federal Bureau of Investigation in New York.

Then why have there been no arrests?

The F.B.I. man cited First Amendment issues. Mr. Kelly said the threat had not risen to the level of a crime. But it did not mean that police investigators “weren’t taking it seriously,” said Paul J. Browne, a spokesman for Mr. Kelly. The department was already monitoring Revolution Muslim and had stepped up its presence at the Manhattan office of Comedy Central, Mr. Browne said.

Arthur Eisenberg, legal director of the New York Civil Liberties Union, said “true threats” enjoyed no First Amendment protection. However, he said, “this rule is easily stated but hard to apply.”

Revolution Muslim is said to have no more than about a dozen members, some of them converts to Islam and considered way over the top by many fellow Muslims. In assessing the threat, Mr. Eisenberg said, much depends on the probability of follow-through, on how afraid the target should realistically be, on whether “there’s any imminent likelihood” of some nut’s being incited to murder by the Web posting.

“I thought Kelly’s statement was telling,” Mr. Eisenberg said. “Presumably, he has facts that we don’t have” to conclude that the threshold of “true threat” had not been crossed.

Here’s hoping. Unfortunately, recent history is studded with episodes in which extremists resorted to murder because they felt that Islam had been wronged. This isn’t a situation where the authorities would want to find out too late that they guessed wrong.