Doubts have been raised about Dominique Strauss-Kahn’s accuser. (REUTERS)

A wealthy public figure accused of sexual misconduct in a swanky hotel says that the charge is trumped up, that his alleged victim lacks credibility.

In their eagerness to bag a famous name, the defendant says, investigators have rushed to judgment. He says they have failed to carefully consider whether the woman who reported being accosted had a motive to lie.

That’s what Dominque Strauss-Kahn says, through his attorneys.

And that’s what lawyer A. Scott Bolden says. He represents Washington Redskins lineman Albert Haynesworth, awaiting trial on a misdemeanor charge that he indecently groped a waitress at the posh W Hotel in Washington.

“Let me tell you something about sex-crimes prosecutors,” said Bolden, a former sex-crimes prosecutor. “They tend to be true believers. I mean, they’ve never met a victim they don’t want to save or who they don’t believe. . . . And when credibility issues arise, they tend to just want to explain them away.”

As authorities Friday acknowledged doubts about the credibility of Strauss-Kahn’s accuser in New York, and the rape case against the former head of the International Monetary Fund seemed in jeopardy, Bolden and other lawyers said the news highlights one of the thorniest issues in sex-crimes prosecutions:

Will jurors believe the alleged victim?

Sometimes the believability issue has nothing to do with the allegation itself. The witness may have a troubled past that could cast doubt on her testimony.

Harry O’Reilly, a retired New York City police detective who helped create the department’s Special Victims Unit in the early 1970s — the unit that handled the Strauss-Kahn case — said investigators often deal with accusers who have less-than-savory backgrounds and who offer changing accounts of alleged assaults.

“It’s quite common for there to be credibility issues,” he said. He said detectives initially should focus only on whether the alleged crime occurred, and not be deterred by the woman’s personal history, even if it involves dishonesty.

“If someone makes an allegation, we listen,” he said. “And then we look for chinks in the story. And if the story begins to dissipate, then we go from there. But at the onset, we’re not looking at things in her past that aren’t relevant to the allegation.”

Attorney Peter Greenspun, who defended Fairfax County teacher Sean Lanigan, acquitted this year of sexually molesting a 12-year-old female student, said authorities have to proceed in such cases with caution.

“These are the kinds of cases where the most care has to be exercised before anyone is charged, because of what allegations like this do to people,” Greenspun said.

Jurors in the Fairfax trial later voiced outrage at the dearth of evidence against Lanigan, a married father of three whose life was shattered by the allegations.

“These are devastating charges,” Greenspun said. “There’s an assumption of guilt by the public, and reputations and life trajectories are destroyed.”

In New York, prosecutors acknowledged that the hotel maid who accused Strauss-Kahn of raping her in his luxury suite May 14 later lied to investigators about her personal history and gave them inconsistent accounts of the moments after the alleged assault.

Strauss-Kahn, 62, who was arrested hours after the allegation and resigned from the IMF, was ordered released from home confinement in Manhattan on Friday. But the district attorney’s office has not moved to dismiss the rape case.

“She said it happened, and he’s sort of a pompous guy with a reputation . . . for grabbing women, so they thought, well, of course, it must have happened,” Greenspun said. He said police generally spend too little time investigating such cases before making arrests, especially when the suspects are prominent men.

Even if Strauss-Kahn’s attorneys have information about his accuser that they could use in court to cast doubt on her veracity, prosecutors have a “moral obligation” to proceed with the case if they believe that the woman is being truthful, said lawyer Mai Fernandez, director of the National Center for Victims of Crime.

“You could have Attila the Hun come to you and say he’s a victim, and the truth of the matter is, in this particular case, he may be,” Fernandez said.

“You have to look first at the evidence that’s directly related to the case at hand,” she added. “The victim? Well, everybody has a past. None of us is without sin. There’s always something that a defense lawyer can use to tarnish your reputation.”

Kristina Korobov, a former prosecutor, agreed with Fernandez, but only to an extent.

“It’s true that you can’t just say to a victim, ‘Well, you have a credibility problem, so too bad,’ and then, based on that, you don’t proceed with the case,” Korobov said. “Because that just rewards offenders who choose victims with credibility problems.”

In a case like Strauss-Kahn’s, she said, prosecutors are probably weighing whether the woman’s credibility is so badly damaged that a conviction would be highly unlikely.

“There were a number of victims in my lifetime who I legitimately believed had been victimized, but I didn’t file a charge,” said Korobov, now a senior attorney with the National Center for the Prosecution of Violence Against Women. “You’ve got to be very selective about what cases you bring, based on what you think you can prove.”