The woman filed a police report with the Columbus, Ohio, police department on Friday morning, accusing Elliott of assaulting her while she was sitting in the passenger seat of a parked vehicle.
Elliott was not arrested and has not been charged with a crime.
The former Ohio State running back denied assaulting the woman and told police that he never lived with her, according to the report.
The woman posted images on Instagram showing what she claimed were bruises caused by Elliott's assault.
The police also reportedly spoke to four witnesses, who all denied seeing an assault.
The Cowboys stated they are aware of the incident but have no comment, per ESPN.com's Todd Archer.
Clarence Hill Jr. of the Fort Worth Star-Telegram added that the team does not believe the allegations to be true.
Elliot turned 21 Friday.