However, those charges were dropped in under 24 hours, because the law under which Ms. Daniels was arrested applied to people who “regularly” appear nude or seminude at a particular establishment, and Ms. Clifford had not appeared at the club consistently.

Still, the episode raised the possibility that the arrest of Ms. Daniels, who by that time had gained nationwide prominence for her allegations that she had had an affair with President Trump, had been politically motivated and caused some to wonder why undercover vice officers had been sent to the strip club in the first place. The police chief at the time, Kim Jacobs, quickly acknowledged that “a mistake was made” and promised to review “the motivations behind the officers’ actions.” (An internal review later found that allegations that there had been a political motivation behind the arrest of Ms. Daniels were “not sustained,” but the review did determine that the arrest was improper.)

Mr. Mitchell, a 31-year veteran of the Division of Police, was not one of the four detectives involved in Ms. Daniels’s arrest on July 11, the police spokeswoman, Sgt. Chantay Boxill, said on Wednesday. Sergeant Boxill said the arrest was one of several episodes that drew attention to the vice unit and eventually prompted an investigation into it.

In August, Mr. Mitchell was investigating a prostitution complaint when he fatally shot 23-year-old Donna Castleberry, the police said. According to police reports, Mr. Mitchell shot Ms. Castleberry multiple times while she was in his car after she stabbed him in the hand. (An investigation into Ms. Castleberry’s death is expected to go before a grand jury in April.)

In September, the vice unit, which at the time consisted of about 20 officers and supervisors, paused operations for a month while the division conducted an internal review of the unit. Asked at a news conference at the time whether the strip-club episode involving Ms. Daniels or the fatal shooting of Ms. Castleberry had resulted in the pause, Chief Jacobs said that “everything’s related to it.”

As the four-week review period came to a close, Chief Jacobs requested that the F.B.I.’s Public Corruption Task Force take over the review — a request the bureau accepted. The pause on the vice unit’s work remained in effect, the police division said at the time.

Based on the F.B.I.’s initial findings, three officers, Steven Rosser, Whitney Lancaster and Mr. Mitchell, were, at various points late last year, stripped of their guns and placed on desk duty pending the outcome of the investigation, Sergeant Boxill said on Wednesday. She added that the investigation was continuing.