When the sexual assault case against Dominique Strauss-Kahn began, his accuser and prosecutors were natural allies. Less than two months later, the relationship has crumbled into tension, with each side feeling betrayed.

Prosecutors have publicly said the woman has a history of lying that has seriously weakened the case. Her lawyer has called the district attorney vacillating, says prosecutors have scurrilously discredited the woman and is calling for a special prosecutor.

As Manhattan prosecutors weigh whether to go ahead with the case, the broken trust between them and their key witness is a thorny problem amid a public debate over their handling of the case. Influential former district attorney Robert Morgenthau weighed in Thursday to praise successor Cyrus R. Vance Jr.’s stewardship of the case, while immigrants’ and women’s advocates gathered outside the courthouse to complain that prosecutors had forsaken an immigrant hotel maid who spoke out against a prominent man.

Prosecutors remained mum about their plans for the case as Strauss-Kahn lawyer Benjamin Brafman reiterated that the former International Monetary Fund leader had “no intention of agreeing to a plea deal.”

Strauss-Kahn, 62, denies the sexual assault allegations. His lawyers want prosecutors to drop the case, which took a serious hit last week when prosecutors and a law enforcement official disclosed that the woman had lied about her background, misrepresented her actions immediately after the alleged attack and mentioned Strauss-Kahn’s wealth to a friend, among other revelations.

While the woman’s questionable credibility could make her a problematic witness, her fractured relationship with prosecutors could prove to be a still bigger hurdle in a case that would hang heavily on her cooperation, experts said.

“(Prosecuting) sex crimes is based on a rapport and trust” that needs to run both ways between victims and prosecutors, said Robin Sax, a former Los Angeles sex-crimes prosecutor now in private practice.

At the outset, that rapport was robust in the Strauss-Kahn case.

After the 32-year-old woman told authorities that Strauss-Kahn attacked her when she came to clean his hotel suite on May 14, prosecutors emphasized her “compelling” and “very powerful” account of a violent encounter. Concerned for her protection and privacy, they have provided her with housing, transportation and meals.

But the relationship began to fray in early June, when Strauss-Kahn’s accuser told prosecutors she had lied about her experiences in her native Guinea -- including a moving, made-up account of being gang-raped there, they said later.

The woman’s lawyer, Kenneth Thompson, has said she broached the subject voluntarily, and he cut off her interview with prosecutors after angry questioning brought her to tears.

The woman wouldn’t meet with prosecutors again for about two weeks, the official said. When she did, she told them she’d gone on cleaning rooms before reporting the alleged assault, though she’d told a grand jury she fled to a hallway to wait for a supervisor, prosecutors have said.

Prosecutors also had learned by then about tens of thousands of dollars’ worth of poorly explained deposits others had made in her bank account, and they found out the next day about her remark about Strauss-Kahn’s money, said the official, who spoke on condition of anonymity to discuss details not made public in court.

Two days later, a prosecutor told a judge on July 1 that “the strength of the case has been affected by the substantial credibility issues” surrounding the woman, though they noted there still was evidence to corroborate a sexual assault. Strauss-Kahn was freed from house arrest.

Moments later, a furious Thompson denounced the DA’s office to a throng of reporters. The woman had made some mistakes but was being truthful about an attack supported by other evidence, he said.

And Vance, he said, was “too afraid” to try the case.

Days later, Thompson called on Vance to recuse his office from the case and arrange for a special prosecutor. In a letter Wednesday that a Thompson spokeswoman provided to reporters, he noted that one of Strauss-Kahn’s lawyers is married to one of Vance’s top assistant prosecutors; the DA’s office says she has recused herself from the case. Thompson also accused the DA’s office of leaking damaging information about the woman to the media “to undermine the veracity of the victim.”

Vance’s office bristled at Thompson’s remarks and brushed off the recusal request as “wholly without merit.”

Generally, special prosecutors are appointed in New York when a DA has a personal conflict of interest, such as having represented a defendant while in private practice, said Bennett L. Gershman, a Pace Law School professor who worked for a special state prosecutor investigating corruption in the 1970s. Gershman called Thompson’s request “a stunt.”

Thompson wasn’t available Thursday for an interview.

As former assistant federal prosecutor, Thompson tried an infamous case surrounding a hideous attack on Haitian immigrant Abner Louima in a police station. One officer pleaded guilty mid-trial to sodomizing Louima with a broomstick; another was ultimately convicted of perjury; two others were convicted of obstruction of justice, but their convictions were overturned.

In private practice, Thompson has represented clients including people injured in a steampipe explosion near Grand Central station and a woman at the center of a domestic violence case involving a top aide to former Gov. David Paterson. The aide, David Johnson, pleaded guilty to harassment.

Thompson’s firm, now Thompson Wigdor, was sanctioned $15,000 in May in a federal employment discrimination case. Manhattan federal Judge William Pauley found that a former partner in the firm, Scott Gilly, and an associate let a client testify falsely in a deposition to get a better settlement. Thompson, who wasn’t involved in the suit, said the firm took steps to make sure such a problem wouldn’t recur.

While it’s unusual for an alleged crime victim’s lawyer to call out a DA so aggressively during a case, an attorney’s job is “zealously to represent the interest of his client,” said Stephen Gillers, a New York University School of Law professor who specializes in regulation of the legal profession.

As for prosecutors, it’s hardly ideal but not entirely surprising to find themselves at odds with an alleged crime victim, said Ellen Yaroshevsky, a legal ethicist and former criminal defense lawyer at Yeshiva University’s Benjamin N. Cardozo School of Law.

“Prosecutors are in a conflicted position to begin with,” she said “because they have an obligation to assess the credibility of a victim, and at the same time, they want to support her.”

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