Captain Fritz & co. knew very quickly that day that Mr Oswald had been at the front entrance at the time of the shooting. 'Now calm down, son, we know you didn't do the actual shooting. But we also know that you were involved. And that's why you're here.'
Later that night:
REPORTER: Did you kill the President?
MR OSWALD: No. I have not been charged with that. In fact, nobody has said that to me yet. The first thing I heard about it was when the newspaper reporters in the hall axed me that question.
From the Warren Report (p. 201):
"At this time Oswald had been arraigned only for the murder of Patrolman Tippett (sic.), but questioning by Captain Fritz and others had been substantially concerned with Oswald's connection with the assassination."
Had Mr Oswald known what DPD were telling the world---------that he was the sixth-floor shooter----------he would have screamed his alibi at the press at every opportunity.