The trial is expected to last between four and six weeks, according to Judge Max Wiley.
Penny, 25, has pleaded not guilty to the charges of second-degree manslaughter and criminally negligent homicide in connection with Jordan Neely's death.
Wiley denied Penny's bid to dismiss his involuntary manslaughter case in January.
Penny put Neely, 30, in a fatal chokehold "that lasted approximately 6 minutes and continued well past the point at which Mr. Neely had stopped purposeful movement," prosecutors with the Manhattan District Attorney's Office have said.
Penny's attorneys have said that they were "saddened at the loss of human life" but that Penny saw "a genuine threat and took action to protect the lives of others," arguing that Neely was "insanely threatening" to passengers aboard the F train in Manhattan.
Witness accounts differ on Neely's behavior in the train, prosecutors say.
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They note that many witnesses relayed that Neely expressed that he was homeless, hungry and thirsty, and most of the witnesses recount that Neely indicated a willingness to go to jail or prison.
Some witnesses report that Neely threatened to hurt people on the train, while others did not report hearing those threats.
Some witnesses told police that Neely was yelling and harassing passengers on the train; however, others have said though Neely had exhibited erratic behavior, he had not been threatening anyone in particular and had not become violent.
Some passengers on the train that day said they didn't feel threatened -- one "wasn't really worried about what was going on" and another called it "like another day typically in New York. That's what I'm used to seeing. I wasn't really looking at it if I was going to be threatened or anything to that nature, but it was a little different because, you know, you don't really hear anybody saying anything like that," according to court filings by the prosecution.
Other passengers described their fear in court filings. One passenger said they "have encountered many things, but nothing that put fear into me like that." Another said Neely was making "half-lunge movements" and coming within a "half a foot of people."
Neely, who was homeless at the time of his death, had a documented mental health history and a history of arrests, including alleged instances of disorderly conduct, fare evasion and assault, according to police sources.
READ MORE | Daniel Penny says he was protecting himself, other passengers from Jordan Neely
Less than 30 seconds after Penny allegedly put Neely into a chokehold, the train arrived at the Broadway-Lafayette Station: "Passengers who had felt fearful on account of being trapped on the train were now free to exit the train. The defendant continued holding Mr. Neely around the neck," said prosecutor Joshua Steinglass in a court filing against Penny's dismissal request. Wiley denied all motions to suppress evidence on Oct. 4.
Footage of the interaction, which began about 2 minutes after the incident started, captures Penny holding Neely for about 4 minutes and 57 seconds on a relatively empty train with a couple of male passengers nearby.
Prosecutors said that about 3 minutes and 10 seconds into the video, Neely ceases all purposeful movement.
"After that moment, Mr. Neely's movements are best described as 'twitching and the kind of agonal movement that you see around death,'" the prosecutor said.
The defense argued Penny had no intent to kill, but Steinglass noted that the second-degree manslaughter charge only requires prosecutors to prove Penny acted recklessly, not intentionally.
"We are confident that a jury, aware of Danny's actions in putting aside his own safety to protect the lives of his fellow riders, will deliver a just verdict," said Penny's lawyers, Steven Raiser and Thomas Kenniff, after Penny's request to dismiss the charge was denied.
"Danny is grateful for the continued prayers and support through this difficult process."
Penny has raised more than $3 million for his legal defense fund ahead of the trial.
Donte Mills, the attorney for Neely's family, issued a statement, saying, "This case is simple. Someone got on a train and was screaming so someone else choked them to death. Those two things do not and will never balance. There is no justification. Jordan had the right to take up his own space. He was allowed to be on that train and even to scream. He did not touch anyone. He was not a visitor on that train, in New York, or in this country. Jordan was allowed to exist and Penny ceased his existence solely because Penny believed he was more important than Jordan."
ABC7 Chicago contributed to this report.
The video in the player above is from a previous report.