This question keeps coming up, and typically generates the same responses, many of which can be quite dangerous for folks to follow. Please keep the following in mind:
1) The responding LE agency is there to stabilize the situation and to determine if a crime occurred. If its immediately apparent that the shooting was justified, they're your friends, if its immediately apparent that the shooting is bad, they're not your friend. If it's not immediately clear which is which (and this is typically the case), it can go either way. I've responded to hundreds of defensive force cases, with about twenty of them being shootings. None of the shooters went to jail. There were two non-shooting cases where the alleged victims went to jail. Don't fall for the hogwash that you're going to be arrested simply because there was a shooting. The numbers clearly show otherwise.
2) Shootings are traumatic events and there is a long history showing that folks affected by the event don't fully consider the import of their speech following the event (and this applies equally to LEOs and non-LEOs). Once words are spoken, they can't be retracted, and it's very difficult to correct them for context.
3) You most certainly have a moral obligation to protect the safety of others in the area, and if you review New York v Quarles, probably also have a legal obligation to the same. The Quarles case gave rise to what has been termed the "Public Safety Statement." The "Public Safety Statement" consists of that information that is immediately needed by responding officers to secure the scene, locate potentially injured parties, and to secure suspect(s). In Quarles, the U.S. Supreme Court held that immediate need for the safety information trumped the right to remain silent. Although the term "Public Safety Statement" is most often used in the context of a LEO shooting, the case law origins make it equally applicable to private person shootings. Please note that the reason you elected to employ deadly force does not meet the criteria for inclusion in a "Public Safety Statement." Don't have that discussion at the scene.
4) The absolute worst thing to say is "I was in fear for my life." There's a couple of reasons why this is so stupid. First, there is absolutely no reason for you to explain the reason for employing deadly force at the scene. Let that one wait until you've met with your attorney. Secondly, that statement invites the follow-on question of "Why were you in fear for your life?" If you answer, then you're having a discussion that's premature. If you don't answer the question, then your silence can be taken as an "Adoptive Admission" (please refer to Salinas v Texas). Why put yourself in such a dilemma if you don't have to?
5) A shooting incident does not end with the last shot being fired. You need to ensure the safety of the scene until officers arrive, and then ensure a smooth transition. Expect that the LEOs will take the lead in managing the transition.
6) When you put all of the above together, you get to the best possible post-shooting advice. This is what nearly every LE agency instructs their officers, and it's equally good advice for everyone else. When involved in a shooting: 1) Manage the scene, 2) Get first responders (LE and Medical) rolling. 3) Give a deliberated "Public Safety Statement" to the first responding LEOs. 4) Do not make any additional statements until you have conferred with counsel. A good attorney will not tell you what to say. The value in a good attorney is that they can illustrate the shortcomings of your words, and the degree to which your words can be taken out of context.