Floyd and Chauvin both worked security at a nightclub at the same time. Coworker David Pinney said the two men had a history.
"They bumped heads," Pinney said.
"How?" CBS News asked.
"It has a lot to do with Derek being extremely aggressive within the club with some of the patrons, which was an issue," Pinney explained.
The Floyd family says they believe what happened on May 25 was in part personal. Their lawyer has called for Chauvin to be charged with first-degree murder, "because we believe he knew who George Floyd was."
"Is there any doubt in your mind that Derek Chauvin knew George Floyd?" CBS News asked Pinney.
"No. He knew him," the coworker said.
"How well did he know him?" CBS News asked.
"I would say pretty well," Pinney replied.
Maya Santamaria, the owner of the now protest-torched club, described how Chauvin treated black patrons when she talked to CBS News for the upcoming special Justice for All.
Santamaria said she had been paying Chauvin, when he was off-duty, to sit in his squad car outside El Nuevo Rodeo for 17 years. She said Floyd worked as a security guard inside the club frequently in the last year. In particular, they both worked on Tuesday nights, when the club had a popular weekly dance competition.
"Do you think Derek had a problem with black people?" CBS News asked.
"I think he was afraid and intimidated," Santamaria said.
"By black folks?" CBS News clarified.
"Yeah," Santamaria confirmed.
As the investigation continues, other cities across the country are considering police reforms. On Tuesday, New York Gov. Andrew Cuomo said he would support sweeping reform measures in his state, including a ban on police chokeholds.
"It's a moment to do real reform and real change," said Cuomo.
City officials in Minneapolis are discussing defunding or dismantling the police department. What happened there has sparked demands for a new law enforcement model. But even those who support the idea aren't sure what that really means.