Bauer, 41, was arrested last week in Montgomery on charges including sodomy and sexual abuse of a child under 12. The AP is withholding some details of the allegations to protect the girl's identity.
Bauer remained jailed Wednesday on $145,000 bail, and court records do not list an attorney who could comment on his behalf. An attorney who represented Bauer in challenging his ouster from the FBI did not respond to requests for comment.
The FBI declined to say whether it was asked for any information about Bauer's suitability to be hired by the state police.
Alabama Govenor Kay Ivey's office referred questions on the matter to the state police, which did not respond to repeated queries about the details of Bauer's hiring.
"You have to ask yourself why an agent from the FBI would want to leave after 10 years," said Lou Reiter, a policing consultant and former deputy chief with the Los Angeles Police Department. "They obviously didn't do any kind of due diligence with their background check."
"There have to be phone calls," added Michael Avery, a retired professor at Suffolk University's Law School and an expert on police misconduct.
Bauer resigned from the state police after his arrest, citing "personal reasons".
Bauer is the latest — and perhaps most extreme — example yet of an FBI agent accused of sexual misconduct moving on. An AP investigation last year found a pattern of FBI supervisors avoiding discipline — and retiring with full benefits — even after claims of sexual misconduct against them were substantiated.
"Nobody wants to take responsibility," the former co-worker who accused Bauer of rape told the AP, which does not typically identify those who say they are the victims of sex crimes. "I didn't want this to happen to anybody else."
An Air Force veteran, Bauer was a member of the Montgomery police force before joining the FBI in 2009, working a number of high-profile cases in the New Orleans field office. He has disputed the sexual misconduct claims made by his FBI co-worker, telling colleagues the acts were consensual.
FBI brass considered the misconduct case to be "egregious", according to a former senior law enforcement official with direct knowledge of the matter. Internal investigators interviewed several female FBI employees about their dealings with Bauer and believed the truth to be "somewhere in the middle" of what Bauer and the co-worker claimed, the former official said. The internal inquiry found Bauer violated FBI policy, including by having sex in an FBI vehicle.
"He flat-out needed to lose his job, and he really should have been charged criminally," said the former official, who wasn't authorised to discuss personnel matters and spoke on condition of anonymity.
Bauer's co-worker told AP that Louisiana authorities had been pursuing criminal charges in St Tammany Parish, north of New Orleans, but she didn't believe she had enough evidence to go forward.
The allegations also played out in a restraining order obtained by the co-worker that names Bauer and had been in the public record in Louisiana for a year when Alabama hired him as a trooper. In it, the woman accuses the lawman of choking her, adding she was "scared for my life".
Bauer was ordered to surrender his "firearms, weapons, swords and knives" as part of the case.
"I couldn't see any more and felt my legs go out from under me," the woman wrote in her application for the order. "He told me many times if I went to war with him I would lose. He told me many times he would destroy me."
The woman told AP that Bauer sexually assaulted her so frequently her hair began to fall out.
"It was a year of torture," she said. "He quite literally would keep me awake for days. I couldn't eat. I couldn't sleep, and in six months I went from 150 pounds to 92 pounds. I was physically dying from what he was doing to me."
- AP
