In the video, provided to ABC News by a restaurant two blocks from the scene of the shooting, a Hummer resembling the police's description of the alleged shooter's car appears to stop suddenly, seemingly bumped by a car that matches the description of Smith's Mercedes SUV.
Then, as the Hummer appears to pull over, the SUV speeds off. Seconds later, the Hummer takes off, apparently following the SUV.
Police have not confirmed the video, according to the New Orleans Police Department.
"This is an ongoing criminal investigation and we don't have anything further to provide at this time," police spokesman Tyler Gamble told ABC News this morning.
Police have said the deadly shooting began when Smith, a former New Orleans Saints star, 34, was rear-ended while driving in the Lower Garden District Saturday night, causing him to hit a vehicle in front of him. The driver of the vehicle that hit Smith, identified by police as Cardell Hayes, then "exchanged words" with Smith, authorities said.
Hayes, 28, then drew a handgun and shot Smith several times, police said.
Hayes stayed at the scene, police said, and was arrested and charged with second-degree murder.
On Sunday, a judge set bond for Hayes at $1 million. He did not enter a plea.
John Fuller, Hayes' attorney, said Monday that Hayes felt threatened and plans to plead not guilty. He also said that Hayes did not know the victim.
Smith's wife, Racquel Smith, was also shot during the incident. Police said her injuries were not life-threatening.