He was not taken to hospital for toxicology until late morning or early afternoon on the 14th. Many hours after Reeva was killed.
I don't have an explicit link, all I could find was this:
http://bigstory.ap.org/article/pistorius-involved-shooting-home-woman-dead-0
'Hours later after undergoing police questioning, Pistorius left a police station accompanied by officers. He looked down as photographers snapped pictures, the hood on his gray workout jacket pulled up, covering most of his face.'
He had come from an afternoon party. I have always thought alcohol was a catalyst in his actions, it is the only thing that makes sense to me that he would so quickly and irrationally go off into a rage.
I would chalk it up again to police ineptness that a blood alcohol test was not done immediately.