The principals are all long dead, so it's unlikely there will be a firm conclusion in the absence of some surprise evidence lurking somewhere, but it's pretty much accepted by most historians that it was a Goering operation. Nikolaus Wachsmann makes the interesting suggestion that Hitler's initial hysteria over the thing was perfectly genuine because Goering didn't tell him for at least 24 hours. After that, the big roundup of political opponents and the opening of the first generation of the camps, all but one of which (Dachau) were run by the SA. The next wave would be all SS.
Is it?