WASHINGTON — Aided by video captured by dashboard cameras in police cruisers, Supreme Court justices on Tuesday seemed poised to rule for police officers involved in a high-speed chase that ended with the deaths of the fleeing driver and his passenger.

No one on the court appeared willing to affirm an appeals court ruling allowing a civil lawsuit by the driver’s daughter to proceed against six West Memphis, Ark., police officers.

They fatally shot driver Donald Rickard and passenger Kelly Allen in 2004 in a chaotic scene on a Memphis street following a chase that began across the Mississippi River in Arkansas. A police officer pulled over Rickard’s white Honda because a headlight was out. Rickard sped away when the officer asked him to get out of the car.

The lawsuit says police used excessive force. But several justices said the officers may not have done anything wrong or at least should be shielded from liability.

The justices don’t often question the facts that underlie the lower court rulings that are at issue before them.

But for the second time in recent years, police video of a car chase seemed to make at least some justices more willing to do their own fact-finding. Police fired 15 shots into Rickard’s car, of which 12 came after Rickard managed to begin driving away from officers who had surrounded the vehicle.

“I mean, when I look at the film, I thought well, sure, he’s going back to the highway. You say we want to show that the policeman knew he wasn’t. I didn’t see any evidence showing that,” Justice Stephen Breyer told Gary Smith, the lawyer for Rickard’s daughter.

The video involved in the case was not shown in the courtroom on Tuesday, but justices had seen it as part of filings with the court.

In 2007, the court voted in a case from Georgia that police may use tactics that put fleeing suspects at risk of death in order to end high-speed car chases. In that case, Justice Antonin Scalia chastised an appeals court panel for its ruling in favor of the driver, who was paralyzed after police bumped his car and forced it off the road.

The driver’s “version of events is so utterly discredited by the record that no reasonable jury could have believed him. The Court of Appeals should not have relied on such visible fiction; it should have viewed the facts in the light depicted by the videotape,” Scalia said.

On that court, only Justice John Paul Stevens, then 87 and the longest-serving justice, said he wasn’t especially frightened by the chase and would have sided with the driver.