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 qualified for Sunday’s men’s 200m final by finishing behind world champion Noah Lyles with a time of 20.20 secs.