Lohan, 26, was detained by police at 2:25 a.m. Wednesday as she left the Dream Hotel, a 315-room luxury Manhattan hotel with a nightclub.
The pedestrian complained that Lohan's SUV had hit his knee. He called authorities and was treated at a local hospital, police said.
When Lohan returned, she was arrested on suspicion of leaving an accident scene. She was given a citation ordering her to appear in court and then released.
Portions of the surveillance video released by New York police on Thursday show Lohan driving up a ramp near the alley.
The security tape blurs out the identities of pedestrians on the street as Lohan drives by, making it hard to see what's happening.
One pedestrian is seen following Lohan's car as it moves out of view, but it's unclear who that person is.
Sources familiar with the case say that the video should help Lohan's case, because even if she grazed a person, the contact was so minor that she wouldn't have been aware of it.
Lohan retweeted a TMZ story Wednesday evening saying the video suggests the victim exaggerated the incident.
The actress' publicist dismissed the allegations, saying in a statement, "While some of the facts are still being gathered, it appears that this is much ado about nothing."
"We are confident this matter will be cleared up in the coming weeks and the claims being made against Lindsay will be proven untrue," the statement continues.
Back in March, Lohan completed five years of felony probation mandated after two drunken driving incidents in 2007.
But she remains on informal probation for taking a necklace from a Venice jewelry store last year without permission.
Los Angeles city prosecutors said that if she did leave the scene of an accident, an L.A. judge could determine it was a violation of her probation terms, which could mean more jail time or community service.
Lohan has been trying to put her much-chronicled legal troubles behind her and resume her acting career with the TV movie "Liz and Dick."