Not being a lawyer or someone who has been in any way involved in a self-defense shooting or even situation, I cannot speak as to whether or not this is good advice, but it is advice:
If the gun owner is involved in a shooting, the first, last and only words to the police should be, “I cannot talk to you until I have consulted with my attorney.” This statement is not obstructionist, does not imply guilt, and does not make the gun owner anti-law enforcement. Just keep in mind that it is not the job of the police or prosecutor to “clear” the gun owner. While the police and prosecutor do have an underlying duty to do justice, keep in mind that the first job of law enforcement is to document and prosecute crimes. They are under no duty to help you establish your claims of self-defense.
You can get the book that excerpt came out of here, but it is definitely something to consider – after massively high-stress situations (like, for example, self-defense scenarios), humans are notoriously unreliable, mentally and physically unbalanced, and arguably in shock. While you are coming to terms with the personal, social, legal, and moral ramifications of what you just experienced in a self-defense situation, what would your intended response to police be?