“For a film that purports to be about the besmirching of someone’s reputation to proceed to smear Ms. Scruggs and the paper she reported for in this manner is highly offensive,” said the letter, which was also signed by Cox Enterprises, the owner of the newspaper and one of the country’s largest cable companies. Cox hired the litigator Martin D. Singer, known for his work on behalf of celebrities like Charlie Sheen and Bill Cosby, to represent the paper.

Warner Bros. fired back with a statement that said, “It is unfortunate and the ultimate irony that The Atlanta Journal-Constitution, having been a part of the rush to judgment of Richard Jewell, is now trying to malign our filmmakers and cast.”

Weeks before the film’s release, The Journal-Constitution published an article headlined “The Ballad of Kathy Scruggs.” It described a “hard-charging” police reporter who used “salty language,” wore “short skirts” and did not leave crime scenes “until her notebook was full.” The article also said the film version of Ms. Scruggs “veers from reality, according to people who knew and worked with her, in suggesting she landed scoops by offering to sleep with sources.”

The film’s bar scene has turned a cinematic examination of privacy, due process and the excesses of the news media into a target for critics who have called it the latest example of Hollywood’s sexist take on women in journalism. The trope of female reporters sleeping with sources or story subjects has appeared in the HBO limited series “Sharp Objects,” the Netflix show “House of Cards” and the movie “Thank You for Smoking,” among other productions.

Kelly McBride, a onetime police reporter who is the senior vice president of the Poynter Institute, a nonprofit organization that supports journalism, said the portrayal of Ms. Scruggs did not reflect reality.

“It is so exceedingly rare,” she said. “And yet this male-dominated world of Hollywood needs to cast female reporters as subject to the whims of nature.”

“I think Clint Eastwood is showing his age, frankly,” she added of the 89-year-old director.

Critics have noted that a film focused on a low point for law enforcement and the press was directed by a prominent conservative at a time when President Trump has vilified the F.B.I. as an arm of the so-called deep state and has repeatedly called the news media “the enemy of the people.”