He writes a memo, several, and that was from what I've read the end of his involvement in the investigation.
Willens has quite a bit to say about Katzenbach (there is a lot more in the book). He was present at the first few WC meetings (until Willens arrived). And yes, you are correct, Katzenbach let the WC do it’s thing as they saw fit.
From “History Will Prove Us Right” by Howard Willens (pages 36 - 37):
By now a veteran of the department’s difficult relations with Hoover, Katzenbach thought the FBI’s leaking the story to favored reporters resulted from their resentment about the appointment of the Warren Commission. In later years, he said, “They very much wanted the report to be made public. They very much wanted to get all the credit for it. They very much wanted the center stage. When that was frustrated, I think they took steps of leaking the information. They have done that in many lesser contexts many, many times when I was in the department.” Katzenbach offered the commission any Justice Department assistance it wanted, but noted that the commission was now fully in charge of the investigation as directed by the president.36 I never thought that the Justice Department abdicated its responsibilities with respect to the investigation of the assassination, as some have suggested. The department certainly had enormous resources—its specialized investigative sections and attorneys, as well as the powers and capabilities of a federal grand jury and the granting of immunity—but I thought that Katzenbach had it right. Initiation of a public investigation by the Department of Justice in the days following the assassination would have destroyed the political accommodation that had been reached with the Texas authorities and congressional committees by the creation of the commission. Any such investigation before the FBI completed its work would have clashed with established department practice and with President Johnson’s decision to rely on a commission, rather than the customary federal agencies, to investigate the assassination.
That's an excellent summary: Katzenbach pushed early on for a special investigation that was
independent of the Justice Department and Congress et al. Meaning it would be beyond his possible control. Hoover was leaking the FBI's report - Oswald as lone assassin - because he wanted to assure the public that the FBI, i.e., him, didn't miss a conspiracy. None of this has a thing to do with covering up what they knew. It was protecting their fannies and bureaucratic infighting et cetera. To a conspiracy mindset, of course, it's sinister behind the scenes machinations.
Philip Shenon says (in Cruel and Shocking Act) that Katzenbach approved/signed off as head of DOJ (Bobby Kennedy was still mourning) on the CIA's decision to confine Nosenko without allowing him due process rights or legal appeals. And that he (Katzenbach) was more involved in monitoring the investigations - both the FBI's and WC. But I'm not aware of anything indicating he directed/limited/controlled either investigation.
That Willens book really has some fascinating behind the scenes accounts.