Last Sunday’s Sopranos episode rattled psychotherapists and their patients when Dr. Jennifer Melfi’s (Lorraine Bracco) own therapist revealed to dinner guests that Tony Soprano (James Gandolfini) was Melfi’s patient.

Therapists, we’ve long known, are among the biggest fans of The Sopranos.

So pleased were they with the credible therapy scenes between Tony Soprano, pop culture’s most famous mobster/patient, and the appealing Dr. Jennifer Melfi, played by Lorraine Bracco, that the American Psychoanalytical Association once gave the show and Bracco an award.

But professionally speaking, they could only scratch their heads at the latest developments on HBO’s hit drama, which comes to an end tonight at 9 on HBO.

Last Sunday, just as Tony Soprano’s life seemed to be imploding with dangerous speed — in short, just when he needed some really good therapy — Melfi and her own therapist made some highly questionable moves.

Not only therapists were distressed. Some patients were actually furious when they showed up for appointments last week, said one New York psychoanalyst.

“You wouldn’t believe the outrage I am hearing,” said Dr. Arnold Richards, who’d missed the episode, but was filled in by his patients. He was talking about a serious ethical lapse by Elliot Kupferberg, played by Peter Bogdanovich, at a dinner party full of therapists. Across the crowded table, the character callously revealed — over Melfi’s protests — the identity of her star patient.

“Mind-boggling,” pronounced Richards. “I do not recall ever being told the name of a patient in treatment.”

Colleagues agreed. “That dinner party was just very upsetting to me,” said Dr. Joseph Annibali, a psychiatrist and psychoanalyst in McLean, Va. “What he did was outrageous. He’s never had control of himself, and this just fits in with that.”

WHY DID KUPFERBERG commit such a sin? He didn’t think Melfi should be treating Tony, whom he considered a manipulative psychopath. Be that as it may, his disclosure was “a very egregious ethical violation,” said Dr. Jan Van Schaik, chair of the Ethics Committee at the Wisconsin Psychoanalytic Institute.

“A patient needs to know that what gets said in the doctor’s office stays there,” said Van Schaik, who’s never witnessed such a violation. “I’ve been at gatherings where people talk about patients in a more disguised form. Even that can be inappropriate. A good therapist should do the best they can to protect the anonymity of patients.”

It’s a shame, Van Schaik added, because “prior to Sunday’s episode, The Sopranos was the best portrayal in the popular media of a therapist-patient relationship.” Annibali agreed: “We’re so used to seeing therapists presented as incompetent hacks. Or as people who are more disturbed than their patients!”

What’s been nice about Melfi, the Virginia therapist explained, is that she’s a complex and caring figure — she’s not ideal, but she tries to help Tony even as she struggles with the idea of treating him.

That is, until this last episode, when she . . . dumped him.

“We’re making progress,” Tony protested, genuinely shocked. “It’s been seven years!” But Melfi had reluctantly read a study, brought to her attention by Kupferberg, claiming that therapy doesn’t actually help sociopaths — it further enables their bad behavior by sharpening their manipulative skills. Demoralized, guilt-ridden and almost speechless with hostility, Melfi literally showed Tony the door.

A TIDBIT THAT HAD some therapists buzzing this week: it turns out the study is a real one — albeit hardly new — from authors Samuel Yochelson and Stanton Samenow, psychiatrists specializing in the criminal mind. But the way the fictional Melfi shoved aside her patient was anything but real, therapists said.

“You don’t just drop a patient like a hot potato, even if you conclude they aren’t responding to therapy,” Annibali protested. “She should have taken several months to do it.”

For Richards, the development just didn’t ring true. After seven years, “only NOW she figures this out? My sense is that there was some narrative purpose for [series creator David] Chase to end this relationship.”

As in the fact that there’s only an hour left to the entire story? That Tony’s life is crashing down around him, and one by one, by death or rejection or his own murderous hand, he appears destined to lose everyone close to him?

Maybe. But Annibali said he’d heard that Bracco may be appearing in the final episode next Sunday. Which means there may still be time to reverse her professional missteps.

“My hope,” Annibali said, “is that she and Tony will get together again.”

But for one certified expert on both therapy AND The Sopranos, that wouldn’t make sense, dramatically speaking. Around halfway through the show’s run, Tony’s therapy started failing, said Dr. Glen Gabbard, professor at the Baylor College of Medicine in Houston and author of The Psychology of The Sopranos.

Perhaps it was because Chase himself went through years of therapy, and has publicly expressed ambivalence about its usefulness. In any case, at the busy psychiatry clinic where Gabbard works, the talk has been about how Melfi should have ended things with Tony years ago.

“The therapy had to end,” Gabbard said. “It was getting more and more futile.

“He’s just not getting any better.”