The unusual request was the latest twist in a closely watched case that, for more than a year, has been filled with complications for prosecutors.

In a letter to Justice Danny K. Chun, Nancy Hoppock, the chief assistant district attorney, acknowledged three issues that have emerged since the detectives, Richard Hall and Edward Martins, were charged in October 2017: that a prosecutor in her office “was involved in a romantic relationship” with one of the detectives; that the accuser “has made a series of false, misleading and inconsistent statements” about the facts of the case; and that because she made those statements, prosecutors cannot call on her to testify and “may not be able to proceed in an ethical fashion on some counts now contained in the indictment.”

Hoppock noted that the woman had already made some of the false statements under oath and that prosecutors have had to confront her about them. As a result, the woman harbors “mistrust in the prosecution team” and has shown “hostility toward our office,” Hoppock wrote in the letter, adding that the woman has publicly expressed her displeasure to news reporters and through social media.

The problem, Hoppock argued, is that if, given all this, prosecutors “decide to drop certain counts against the defendants,” they will be perceived as “unfairly disfavoring” the woman and favoring the police.

“We regret that our continuing to pursue the case might well create an appearance of impropriety and discourage public confidence in our office and the Kings County criminal justice system,” Hoppock wrote. “In the end, we want to see justice done.”

The letter was submitted two days after a lawyer for the detectives, Mark A. Bederow, also filed documents in court seeking a special prosecutor for the case. Bederow wrote that the district attorney’s office “must be disqualified from prosecuting this case due to the existence of numerous conflicts of interest.”

In a telephone interview, Bederow said the letter submitted by prosecutors on Thursday made “it abundantly clear that they do not believe” the woman and “want nothing to do with the further prosecution of this case.”

“They can’t continue to prosecute this case when they’re calling her a liar and she’s accusing them of corruption,” Bederow said. “We certainly hope that whoever steps in to evaluate this case will make appropriate decisions based upon the evidence, not based on external influences and politics.”

The district attorney’s office obtained indictments against Hall and Martins in the fall of 2017, just as the #MeToo movement was gathering momentum. Hall and Martins have since quit the police.

Prosecutors have alleged that the detectives stopped the woman for having marijuana in her car on Sept. 15, 2017, handcuffed her and put her in their police van. Then, during a drive through southern Brooklyn, the woman has said, Hall forced her to perform oral sex and Martins raped her.

Prosecutors have said they have DNA samples proving there was a sexual encounter, which Hoppock reiterated in her letter Thursday.

From the start, though, the case has not only been filled by shocking allegations against the detectives, but punctuated by an unusually aggressive effort by the defendants’ lawyers to point out numerous holes in the accuser’s story.

While lawyers for Hall and Martins have never said explicitly that the encounter was consensual, they have moved twice — unsuccessfully — to dismiss the indictment, claiming that the prosecutors allowed the woman to lie in front of a grand jury, and that her story of assault is “uncorroborated.”

The defense lawyers have also contended that the woman has repeatedly changed her account of the attack, including the clothes she was wearing, the make and model of the vehicle she rode in and which of the defendants assaulted her first. More recently, they have presented cellphone evidence that they say shows that neither detective was near where the woman has claimed they drove her during the alleged assaults.

It is a common phenomenon for rape victims, because of shame or trauma, to make incomplete or inconsistent statements in the hours — even days — after their attacks. Although her statements to police did contain contradictions, the woman at the center of the charges against the two detectives has never wavered in her insistence that they forcibly raped her, court papers show.

This article originally appeared in The New York Times.