A police report said footage appeared to show Coleman being shoved into a wall, before Richardson threw an item at him.
She was released on Monday following the incident.
Coleman did not want to participate in the investigation and “declined to be a victim”, the police officer’s report reads.
Richardson refused to speak to waiting reporters after her heat in Eugene, instead wishing them a “blessed day”.
Following her arrest, USA Track and Field said it was “aware of the reports” but would “not be commenting on this matter”.
Coleman finished sixth in Sunday’s 200m men’s final, with world champion Noah Lyles claiming first with a time of 19.63 seconds.
“She’s a human being and a great person,” Coleman said about Richardson.
“She’s going to bounce back because she’s the best female athlete in the world.”
Melissa Jefferson-Wooden ran a personal best of 21.84 seconds in the women’s 200m final to complete a sprint double after clinching the 100m two days earlier.
