Smith says both jailers who spoke with Bland, who was black, insisted that she appeared fine when being booked on a charge of assaulting a public servant.
Bland's body was found three days later in her cell. Authorities say she hanged herself using a plastic liner taken from a garbage can.
Her family has said she was looking forward to starting a new job at her alma mater, Prairie View A&M University.
In suburban Chicago, Bland's relatives held a news conference to discuss video of the arrest taken from the officer's dashcam, which shows him drawing a stun gun and threatening Bland when she refuses to follow his orders.
"I simply feel like the officer was picking on her. Point-blank, period. I personally think that it's petty," Sharon Cooper, Bland’s sister, told reporters, adding that she thinks he got angry because "his ego was bruised."
Bland's family also says she was not acting suicidal. Family attorney Cannon Lambert said Wednesday that Bland had just bought groceries and was ecstatic about her new job when she was pulled over.
Lambert said the family had no indication that Bland was ever treated for epilepsy.
Her body was flown back to Chicago in preparation for a funeral on Saturday.
The video posted online Tuesday by the Texas Department of Public Safety shows the trooper, who is white, stopping Bland for failing to signal a lane change. After he hands her a written warning, the trooper remarks that Bland seems irritated. The Illinois woman replies that she is irritated because she had changed lanes to make way for the trooper's car.
The conversation quickly turns hostile when the officer asks Bland to put out her cigarette and she asks why she can't smoke in her own car. The trooper then orders Bland to get out of the vehicle. She refuses, and he tells her she is under arrest.
Further refusals to get out bring a threat from the trooper to drag her out. He then pulls out a stun gun and makes the threat about lighting Bland up.
Her death comes after nearly a year of heightened national scrutiny of police and their dealings with black suspects, especially those who have been killed by officers or die in police custody.
In response to questions about gaps and overlaps in the video, authorities said the footage was not edited or manipulated.
Tom Vinger, a spokesman for the Department of Public Safety, said glitches occurred in the recording when it was uploaded for public viewing. He said the agency will repost the video.
The trooper, who has been on the force for just over a year, has been placed on administrative leave for violating unspecified police procedures and the Department of Public Safety's courtesy policy. The agency would not address questions about whether the trooper acted appropriately by drawing his stun gun or trying to pull Bland out of the vehicle.
Al Jazeera and wire services
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