The 24-year-old defender is alleged to have been involved in an incident in Faces nightclub whilst out with a number of team-mates.
According to second-hand stories on numerous fans' websites Da Costa is alleged to have drunkenly made a play for a young woman who then rejected his advances. He is then said to have assaulted her and one of her friends.
Da Costa has been bailed until early December whilst Police conduct an investigation into the allegations.