‘‘On Milford beach,’’ Cuddy interjected brightly. ‘‘Collecting seashells.’’ The rookies shifted uneasily side to side. One guy finally asked Cuddy whether she had chosen to be in this unit. No, she said, she was assigned, but she had worked in almost every other unit, and none was as satisfying as this one. Not a lot of people want to be here, she said, because ‘‘90 percent of our cases are kids being drilled in the ass by their grandfathers. But when you lock up their grandfather, that kid will never forget you for being their voice.’’ When the rookies left, five uncomfortable minutes later, I got the feeling that they were all fervently hoping they would never be assigned there, but Cuddy merely rolled her eyes.

The first step to a successful sexual-assault investigation is investigating, which would seem to be a given. All too often, though, that’s not what happens. A recent review of the New Orleans Police Department by the city’s inspector general, for example, found that from 2011 to 2013, five detectives from the sex-crimes unit filed investigative reports in only 14 percent of the sexual-assault and child-abuse cases assigned to them. Most initial reports of assaults were misclassified as ‘‘miscellaneous’’ and simply closed without any investigation at all. In a particularly galling example, detectives closed the case of a 2-year-old who was taken to an emergency room after a suspected sexual assault, and who tested positive for a sexually transmitted disease. The primary detective wrote in his report that the toddler did not disclose any information that would warrant a criminal investigation. The inspector general found that the sex-crimes detectives worked without supervision and closed cases without any review.

In New Haven, unless a victim chooses not to file charges, every case that is assigned to an S.V.U. detective is investigated. According to Segui, the detectives refer about 90 percent of their cases to the state’s attorney’s office for an arrest warrant — though that doesn’t mean they’ll get one. Every recommendation by a detective either to proceed with an application for an arrest warrant or to close a case is first reviewed by Segui, then by the court. The detectives have considerable influence on Segui. ‘‘I trust them,’’ she told me. If the detectives feel they should close a case, she looks it over herself and then occasionally has the prosecutor ‘‘in essence, quote-unquote, check our work.’’

During my months with the unit, the detectives closed six cases out of dozens without applying for an arrest warrant. There was a young woman who told an emergency-room nurse that a friend raped her. Her lip was swollen as if she’d been punched in the mouth. She didn’t want to file a complaint, but Cuddy persuaded her to take the sexual-assault exam, so that they would have the evidence if she changed her mind. A mother reported that her 3-year-old son said her ex-partner bit and pulled his penis, but the boy never disclosed this or any other abuse during his forensic interview. If there’s no medical evidence (there wasn’t), and if a child doesn’t mention abuse during the forensic interview, the case doesn’t move forward. Cuddy also noticed that when the mother was asked to repeat exactly what her son said, she used the word ‘‘penis’’; in his interview, the boy always used the word ‘‘pee-pee.’’

Some cases were so tangled and muddy that the truth remained unknowable, and they eventually withered because of a lack of probable cause. One of these was a case that came back to the unit: an injured woman whom the detectives interviewed in the hospital two months earlier, after hospital personnel called in a case of possible domestic abuse. The victim told the detectives she didn’t know how her face became bruised and bloodied. She had been sleeping at her ex-boyfriend’s house the night before, so she could drive him to work the next morning, and she woke to the taste of blood in her mouth. She said her ex-boyfriend told her she had fallen. She thought maybe he had elbowed her in her sleep. With no claim of domestic abuse, Landisio referred the case back to patrol, and an officer interviewed the ex. That report concluded: ‘‘Due to [complainant’s] conflicting report and no evidence of domestic violence, there was no arrest made. No further actions were taken.’’

But shortly afterward, the victim claimed her ex-boyfriend had beaten and sexually assaulted her, and the case was reassigned to Landisio. ‘‘She definitely got [expletive] up,’’ Landisio said. He was sitting at his desk across from Cuddy, examining a photograph of the woman’s face — the right side was puffy and purpled, the eye sealed shut, as if she’d been lying half-submerged in water. ‘‘Yeah, but how?’’ Cuddy asked. ‘‘That’s the question.’’

Landisio and Cuddy interviewed the victim again, and this time she described her ex asking for sex that night and hitting her after she refused. The last thing she heard before passing out was her clothes being ripped, she said. When Landisio asked her why she didn’t mention the assault before, the woman said it took a few days for the memories to come back to her.