So, I have always told potential clients (everyone) that if they ever shot anyone legally or otherwise, not to make any statements to the police. This Chicago story is a good example of why you shut up. There is nothing you say which will not be used against you. I interviewed the Director of the Texas Department of Public Safety Training Academy a few years ago. He told me that it was the policy of the department to allow 48 hours before interveiwing an officer involved in a fatal shooting. The reason, because of the stress induced by the incident can result in misleading information.
Do you think a civilian involved in a shooting ever got that consideration? Oh hell no. In fact the opposite would be true. Harsh and lengthy interrogation techniques are used readily against persons involved in homicides.