On Friday, Cobb County Police Sgt. Dana Pierce said that Lieutenant Abbott submitted his retirement request, and had it approved, on the day of the news conference.

The Atlanta Journal-Constitution reported that Sam Heaton, Cobb County’s public safety director, said that Lieutenant Abbott “did request an immediate retirement and we have approved his request. He is entitled to his full retirement benefits and would have been even if terminated.”

Sergeant Pierce confirmed that the statement was made by Mr. Heaton, who could not immediately be reached for comment on Friday evening.

Chief Register was appointed to lead the department in June.

The police in Cobb County, which is northwest of Atlanta and is Georgia’s third most populated county, with about 741,000 people, have come under scrutiny for race relations in the past. A report by the International Association of Chiefs of Police gave the department a high community approval rating, but also mentioned a perception of discriminatory and biased policing, WSB reported.

Andrea Young, the executive director for the American Civil Liberties Union of Georgia, said the department should pursue diversity and cultural training. “Under zero circumstances is it ever appropriate to joke about police officers committing murder,” she said in an emailed statement.

The traffic stop took place on July 10, 2016, at about 3 a.m. on Interstate 75 near Marietta, the county seat. The male driver was pulled over on suspicion of driving under the influence, his lawyer, Surinder Chadha Jimenez, said in a telephone interview on Thursday. The woman was a passenger in the car, he said.

Mr. Chadha Jimenez said he had watched the video to prepare for his client’s case. He said that it appeared the officer “didn’t like the way” the woman was talking to him during the arrest of the man, and that “they kept going back and forth.”