To circle back to what agency or agencies might investigate, the California Attorney General might also do so, depending on state law. In a number of states, the state AG can investigate if "invited" to do so by one of several specifically identified persons or agencies (e.g., the governor, a judge, the local prosecutor, etc.). Some state attorneys general also have authority to investigate civil rights violations. The state AGs are not normally intertwined with local law enforcement the way local prosecutors may be.
While I have no beef with police replying with deadly force when fired upon, the issue here is not that simple. Did the police deliberately employ the incendiary gas canisters in a deliberate effort to execute Dorner? Did they allow sufficient time for the regular tear gas take effect? Were there other, reasonable alternatives? In the end, all the police actions may be justifiable but there has to be a fair investigation into the matter.