The parents of a Georgia woman who died after she fell from a moving patrol car following her arrest fought back tears on Friday as they demanded answers in their daughter’s death.

Brianna Grier, 28, suffered significant injuries on 15 July and died six days later at an Atlanta hospital. The Georgia bureau of investigation said this week that the deputies who put Grier in the back of a patrol car to take her to the Hancock county sheriff’s office failed to close the rear passenger-side door before driving away.

“We’re trying to get answers of what really happened … We ain’t trying to start no problem,” a tearful Marvin Grier, Brianna’s father, said during a news conference, his voice catching several times. He was joined by Brianna’s mother and sister, Mary and Lottie Grier.

Grier was arrested after Hancock county sheriff’s deputies were called to a home in Sparta, the GBI has said. The deputies put Grier in the back of a patrol car, but she was not wearing a seatbelt, her hands were cuffed in front of her and the rear passenger-side door was never closed, according to GBI investigators.

The GBI has not said why deputies were called to the home or why Grier was arrested. The prominent civil rights attorney Ben Crump, who is representing her family, said Grier was taken into custody after a mental health crisis.

“Yet again we have another African American citizen killed in just an unbelievable way while in the custody of the police,” Crump said at the Friday news conference in downtown Decatur, a suburb of Atlanta.

He addressed Grier’s parents: “We won’t let them sweep your baby daughter’s death under the rug.”

Crump said his team would investigate what failures caused Grier to fall out of the car while it was moving and suffer a brain injury that put her in a coma until she died on 21 July.

The president of the Georgia State Conference of the NAACP, Gerald Griggs, called on state and county officials for answers.

“To the Hancock county sheriff, it’s time to be transparent,” Griggs said. “It’s time to be accountable. To the GBI, it’s time for y’all to meet with this family. To the governor, it’s time for you to recognize, again, that Georgia has a police accountability problem.”

The GBI has said agents have done interviews, reviewed multiple body camera videos and done mechanical tests on the patrol car as part of the ongoing investigation into Grier’s death.