The 65-year-old Long Island man, David Whelan, was the subject of a Cuomo tirade during a broadcast of "Let's Get After It with Chris Cuomo" over an alleged verbal confrontation between the two on Easter Sunday.
According to the East Hampton police complaint, obtained by The Independent, Cuomo allegedly threatened Mr Whelan, saying he hadn't "seen the last of him" and that "he would beat the crap out" of him.
"At this time D. Whelan does not wish to pursue charges but does want the situation documented as he is worried about C. Cuomo retaliating against him," the report said.
In an interview with The New York Post, Mr Whelan said he approached Cuomo and asked why he wasn't social distancing.
"I said to him, 'Your brother is the coronavirus czar, and you're not even following his rules — unnecessary travel'," he said.
Cuomo has been in quarantine and broadcasting from his Southampton home since announcing on 31 March that he had tested positive for coronavirus.
According to Mr Whelan, Cuomo responded: "'Who the hell are you?! I can do what I want!' He just ranted, screaming, 'I'll find out who you are!'"
"He said, 'This is not the end of this. You'll deal with this later. We will meet again.' If that's not a threat, I don't know what is," Mr Whelan said.
Cuomo vented about the incident during his SiriusXM radio show on Monday, explaining that his public profile prevented him from firing back at people talking "bullshit".
"I want to be able to tell you to go to hell, to shut your mouth," Cuomo said. "I don't get that doing what I do for a living, me being able to tell you to shut your mouth or I will do you the way you guys do each other."
"I don't want some jackass, loser, fat-tire biker being able to pull over and get in my space and talk bullshit to me, I don't want to hear it."
It is the second major controversy to come out of Monday's show, during which Cuomo seemingly had an existential crisis and said he didn't want to work at CNN because he didn't value indulging irrationality and hyperpartisanship.
"I don't like what I do professionally. I don't think it's worth my time," he said.
"I don't think it's worth it to me because I don't think I mean enough, I don't think I matter enough, I don't think I can really change anything, so then what am I really doing?"
Cuomo walked back the comments during his SiriusXM show on Tuesday, saying he was taken out of context.
"I was talking about having legitimate questions, which I've had all along this administration. Let alone, with a fever with Covid for two weeks and being pissed off about being sick and rethinking a lot of things on an existential basis all the time," he said.
CNN did not immediately respond to a request for comment. CNN has previously defended their star broadcaster after video showed him threatening to throw a man down a set of stairs.
The video, shared widely across YouTube and Twitter, showed Cuomo repeatedly cursing and threatening a man in New York in August last year.
"Punk ass bitches from the right call me Fredo," Cuomo says to a man standing beside him. "My name is Chris Cuomo. I'm an anchor on CNN. Fredo is from 'The Godfather.' He was a weak brother and they use it as an Italian aspersion."
After the man says he thought Cuomo's name was Fredo, the cable TV host became agitated, saying: "You're going to have a big fucking problem. I'll fucking ruin your shirt. I'll fucking throw you down these stairs."