Here is a great two-part Youtube series on why you NEVER talk to a cop if you are involved in a shooting... or even involved in some way.
A cops job is to investigate... so just let them... but YOU never speak to them unless your lawyer is present and a few protections are set in place.
Remember... "Anything you say will or can be used against you"... by design, it does not state that it can HELP you (bet you didn't know that)!!!!
Was also part of my CCW/CCH training class here in Kansas (the rule, not the videos).
Part #1 is the lawyers view and part #2 is from a policeman/detective (and they both agree).....
YouTube - Don't Talk to Cops, Part 1
YouTube - Don't Talk to Cops, Part 2
Enjoy.... worth watching it all.....