Arnold, whose Viceland series, The Hunt for the Trump Tapes, is set to premiere Tuesday, tweeted Sunday night that Mark Burnett choked him at the Evening Before the Emmys event and "ran away with his torn pink shirt [and] missing gold chain."
Arnold said he contacted the Los Angeles Police Department about the incident.
Downey offered a different account, tweeting a photo of what appears to be a bruise on her hand.
"Got this bruise tonight when Tom Arnold tried to ambush my husband Mark and me at a charity event. Is your TV show worth it Tom?" Downey said.
Arnold's series deals with the comedian's quest to obtain alleged recordings of President Donald Trump making racist and other disparaging remarks on the set of The Apprentice, which was produced by Burnett. Arnold, a former friend of Trump's, appeared on The Celebrity Apprentice.
Arnold replied to Downey's tweet, calling her account of the incident false.
"You lie your crazy husband attacked me you psycho," Arnold wrote. "I'm filing police report & suing you for defamation."
Arnold later tweeted that documentary filmmaker Bryan Fogel witnessed the attack and "has tape."
The Los Angeles Police Department confirmed it was aware of an incident involving Arnold and Burnett, but no report had been filed.