Footage of the July 10 arrest shows Sandra Bland’s car being pulled over for failing to signal and then an ensuing confrontation with the officer.
The coroner said the woman hanged herself in her cell but her family has demanded an independent autopsy.
State officials and the FBI are both investigating her death.
In the video, released by the Texas Department of Public Safety, the policeman is seen issuing a ticket and then asking Sandra Bland, 28, to stub out her cigarette, which she refuses.
When the woman refuses to step out of the car, he tries unsuccessfully to pull her out. He then appears to threaten her with a Taser and says the words: “I will light you up.”
Sandra Bland gets out of the car and the two of them move out of vision, but the audio suggests the confrontation becomes physical during the arrest before more officers arrive.
The arresting officer said he was kicked. He has been put on administrative leave.
Later the video appears to have abrupt breaks in its continuity and is looped in several places, suggesting it was edited prior to release.
At 25:01 a man is seen walking away from his pick-up truck and out of shot, before reappearing at the door of the vehicle a few seconds later.
Social media users, including award-winning film director Ava DuVernay, have questioned the video’s authenticity.
On July 21, local district attorney Elton Mathis said the case – like all deaths in a jail cell – would be investigated as a murder.
The death of Sandra Bland is one of several under national scrutiny in which a black person has died while in police custody.
Other high-profile cases, since the death of Michael Brown in Ferguson last summer, have sparked protests and sometimes unrest.
On July 21, prosecutors in Cincinnati, Ohio said they were probing the fatal shooting of a black motorist by a white police officer who had stopped him over a missing licence plate.
Samuel Dubose, 43, apparently refused to co-operate with Officer Ray Tensing, leading to a struggle.
He was then shot in the head and pronounced dead at the scene.
The police officer has been placed on paid administrative leave while the investigation continues.
Sandra Bland’s family has ordered an independent autopsy and called for an investigation by the Department of Justice.
Video footage did not show what happened inside Sandra Bland’s cell, but did suggest no-one entered or left it until someone found her unconscious.
Jail Sheriff Glen Smith said his staff checked on her less than an hour before she was found dead.
Sandra Bland’s sister, Shante Needham, said Sandra called her from jail, saying she did not know why she had been arrested and that an officer had possibly broken her arm.
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