Last August, NFL Director of Investigations Kia Roberts emailed a top city official in Columbus, Ohio, where police were investigating allegations Dallas Cowboys running back Ezekiel Elliott assaulted a woman.

Roberts mentioned her background as a former homicide prosecutor in Brooklyn, explained she was also looking into the allegations for the NFL and asked to speak about the police investigation. The Columbus official replied, via email, that he’d let her know when the investigation was over.

Last November — weeks after Columbus prosecutors decided not to charge Elliott and publicly released a cache of documents from the case — Roberts emailed a prosecutor and asked for some of his personal investigative notes. He declined to turn them over. A month later, Roberts emailed the same prosecutor and asked if he would share details of his conversations with Elliott’s accuser. Again, the prosecutor rejected the NFL’s request.

Since being sharply criticized by women’s groups and others for its handling of the Ray Rice case in 2014, the NFL has sought to demonstrate that it takes domestic violence allegations against its players seriously. The league bolstered its security staff, said it would launch its own investigations of reports of abuse committed by NFL players, and deliver punishments that hold abusers accountable regardless of how the criminal justice system handles a case.

[Cowboys owner Jerry Jones defends Elliott ]

The Cowboys owner has defended his star running back. (Michael Owen Baker/AP)

But as the Elliott case shows, there are limits to how aggressive the league can be in investigating claims.

“These are difficult and complex matters as we have all seen in cases across America that go well beyond sports. NFL investigations are thorough and comprehensive as these serious matters deserve,” league spokesman Brian McCarthy said in a statement. “These investigations take time, but we want to be thorough rather than rush to a decision without having all the facts.”

Good idea, tough execution

The NFL’s unsuccessful attempts to pry additional information from Columbus officials, some of which were first reported by Deadspin and are detailed in records released to The Washington Post this past week, illustrate the limits confronting the league’s nascent investigative force as it handles potentially its most vexing case: the one-year-old inquiry into allegations Elliott assaulted a woman last July.

Last year, law enforcement in two cities declined to press charges against the 22-year-old Cowboys star after looking into separate assault complaints made by the same 21-year-old Ohio woman. (The Post generally does not name accusers in cases involving allegations of domestic violence.) Elliott maintains he never harmed the woman; she maintains he did, repeatedly. Cowboys owner Jerry Jones has dismissed the accusations as meritless.

In Columbus, city attorney Rick Pfeiffer treated the NFL’s request for more information, essentially, like a media inquiry.

“Nothing has been determined as of this time,” he wrote Roberts in August, not responding to her request for a phone conversation. “I will let you know our conclusion.”

When Pfeiffer’s office decided it would not press charges last September, it publicly released witness interview transcripts and recordings as well as photos of the accuser’s injuries. Columbus officials alerted Roberts to their decision with an email also sent to more than a dozen journalists.

The materials released in Columbus show why prosecutors decided there was not enough evidence to press charges. The accuser called police early July 22, alleging Elliott had physically abused her repeatedly over the previous week. The woman had bruises on one shoulder and on both forearms and wrists. In violent outbursts, the woman alleged, Elliott had choked her, threw her against a wall and dragged her across a floor. She said Elliott told her “she was lucky that he has not killed her yet,” and that “he loved her and did not want to have to put his hands her but it’s tough love.”

Elliott denied the claims, and told police the accuser had been in a barfight with another woman that night. Police found no witnesses of Elliott’s alleged assaults. Three people, including a security manager at a bar, told police they saw Elliott’s accuser fight another woman that evening, not Elliott. Four people told police they heard the woman yell at Elliott she was going to “call the cops to ruin his career.” And one woman — whom Elliott’s accuser had identified as a witness — told police she didn’t witness any assault, but Elliott’s accuser had asked her to lie and say she had.

An investigation stalled

In late October, Roberts flew to Columbus and met with prosecutor Robert Tobias. A few days later, she emailed Tobias and requested some information that had not been included in the documents publicly released: a calendar the prosecutor had kept, with detailed notes of the accuser’s allegations and when they occurred.

“As we discussed, an important consideration in our investigation is the consistency between the allegations that [Elliott’s accuser] has made to us here at the league, and what she has alleged to you,” Roberts wrote on Nov. 3. Ten minutes later, Tobias replied.

“As mentioned during our meeting, I do not wish to turn over the chart I created,” Tobias wrote. He directed Roberts to listen to the publicly released interview recordings.

A month later, Roberts emailed again. She’d asked the prosecutor to share details of his conversations with the accuser, and Tobias had declined, citing concerns about violating the woman’s confidentiality. Roberts made another appeal, this time including Tobias’s boss.

[Elliott investigation could test NFL domestic violence policy]

“During my conversations with both of you over the last few months, I have mentioned that prior to joining the League, I spent approximately 9 years in the Brooklyn District Attorney’s Office,” Roberts wrote Dec. 9. She mentioned an information-sharing agreement the NFL had recently signed with the National District Attorneys Association.

“I sincerely hope that we can come to an understanding here,” Roberts wrote.

Tobias, in an email exchange with The Post, said he believes he called Roberts minutes later and explained, again, that he would not discuss his conversations with the accuser. Tobias declined to further discuss his interactions with the NFL. The Cowboys and Elliott declined to comment. Elliott’s accuser did not reply to a phone message seeking comment.

As Roberts was wrangling with Columbus officials, a similar process played out in South Florida, where Elliott’s accuser told the NFL a previous incident had occurred.

On Sept. 28, NFL security representative Ed Du Bois emailed several officials at Aventura Police Department seeking “as much information as possible about this matter.”

“The NFL is very aggressive in it’s (sic) investigation of this conduct so please respond as soon a possible,” Du Bois wrote.

Aventura Police treated the inquiry as a public records request, a police spokesman said this past week, and gave the NFL investigator a copy of the incident report, and nothing more.

Credit and criticism

Like the Columbus materials, that report is inconclusive. Police responded to a call the night of Feb. 12, 2016. The accuser alleged Ezekiel pushed her against the wall, causing “left shoulder pain.” Elliott denied the accusation. Officers saw no visible signs of an injury. The woman declined an offer by emergency medical responders to take her to the hospital. The incident did not result in a criminal charge.

The NFL’s investigative limits played a role in its last high-profile domestic violence case as well. Last year, despite an earlier pledge to suspend players found to have abused a spouse or partner for at least six games, Goodell suspended New York Giants place kicker Josh Brown for one game after prosecutors in Washington state declined to press charges stemming from a 2015 arrest for allegedly assaulting his wife.

Last October, controversy erupted after law enforcement released documents showing Brown admitted to being “physically, emotionally and verbally abusive” of his wife for years. NFL officials said their investigators had repeatedly attempted to interview officials in King County, Wash., and review investigative files, but law enforcement refused to release records while the investigation was ongoing.

“We’re not going to release them to anyone, including the NFL,” a King County law enforcement spokeswoman said at the time.

As the NFL’s inquiry has dragged on, Elliott has been involved in two other incidents that Goodell could consider as he decides whether to punish the player. In March, videos emerged of Elliott pulling down a woman’s top during a St. Patrick’s Day celebration in Dallas. And two weeks ago, he was involved in an altercation in a Dallas bar that resulted in no criminal charges.

Some victims’ advocates remain skeptical of the league’s efforts to reduce domestic violence committed by NFL players.

“The NFL never had a Ray Rice problem, it has a violence against women problem, and that problem is the product of Roger Goodell and his board, the owners,” said Terry O’Neill, president of the National Organization for Women. “The investigation is being done to allow Ezekiel to play . . . it’s not about protecting the victim.”

Others give the NFL credit for going further than many private employers to examine allegations of abuse, and acknowledge the difficulties inherent in investigating domestic violence cases.

“I think they’re being thoughtful, and I recognize that they have some barriers to making things happen quickly,” said Ruth Glenn, executive director of the National Coalition Against Domestic Violence. “Any time you’re trying to deal with something this complicated, it’s going to take time.”

Meryl Williams in Columbus, Ohio, contributed to this report.