The alleged assault happened about 11pm and she went to the hospital about noon the next day, going by my memory of the timeline.
The police arrived at his hotel room to talk to him about 11:00pm that next night, or approx 24 hours after the event. He was then escorted for DNA tests about 2am so you know they had evidence from her by then. (And notice how long they're with him before taking him to get his samples.)