Putin was absolutely involved in the poisoning of the KGB agent. He may not have done the poisoning, but of course Putin knew about it. Putin runs everything in that country. He should be held accountable for his death and it should be investigated. Putin is as close to a dictator as you can get.
If there is strong enough evidence to bring a court case, then Putin should have to face judgement for any role he may have had in the poisoning of the former KGB agent who died tragically. Leaders should not order assassinations of their countrymen. Murder is murder, even if committed by a president.
Russia is almost a police state where Putin rules with an iron fist. If the media finds evidence that Putin was responsible for poisoning the former agent, they will never report it because they know that the same thing will happen to them. And even if the Russian people knew about it, there's not much they can do. There isn't really a way to hold Putin accountable because of how corrupt the Russian government is.
There is no doubt he should absolutely be held responsible for his death, aside from any evidence that has been surfacing, the simple truth of the matter is he was the one responsible, it doesnt matter if he administered the poisoning or was simply aware of it, he automatically should be held responsible because he had known about it, direct or indirect, he could have prevented it.
There are a couple circumstances in which Putin would have to take such an extreme measure to resolve them, especially involving an ex KGB agent. Some of these situations include the release of classified information to foreign entities that would endanger Russians or their families, or the possibility of blackmail by the ex-agent in order to get money or power. Both of which would result in a trial and life sentence in Western countries, but, being Russia, the method was a little more direct. I believe that if Putin was acting in the best interests of Russian citizens then he was justified in his (albeit direct and a little crude) actions.