I think he did in that he either ordered the hit or a close advisor to him ordered the hit.
It makes sense to me in the Russian way. Vladimir was the former head of the KGB and used that muscle to get into his position as Russia's Prime Minister or President......apparently interchangeable as history as shown.
Would Putin have the arrogance to assume he could get away with assassinating his opposition? I think yes. Mostly because I think he is in a bit of a panic.
Firstly Malaysia Airlines Flight No. 17 shot down over the Ukraine and then, Saudi Arabia bottoms out oil per barrel prices. Both events destabilised Russia's confidence and their economy. Not to mention economic sanctions.
While in a panic, most people go back to what they know. And the KGB knew how to deal with the opposition in a way that didn't involve courts of law.
Do I think Vladimir Putin will ever answer to this? Probably not. His administration may fall due to something else. But I doubt it's gonna be based on this.
Let's all remember too that Vladimir Putin allowed publicity photos like this during the Sochi Winter Olympics:
If nothing else, that shows a significant disconnect with how the world works.