Based on my training with Massad Ayoob and others, I'd suggest considering the following:
[1] In a high stress, self defense event, a person will usually experience one or more artifacts of the "fight-flight" response that will affect his perception of time, distance and the event in general. So immediately after the event is a lousy time for the person involved to start telling his story. He will frequently make mistakes. He will often get things wrong because of his altered perceptions.
[2] In addition, few people have been sufficiently inoculated to the type of stress involved to be able, immediately after the event, to maintain proper control of their emotions and to give a good and cogent account of the event.
[3] At the same time, while one has a right to remain silent, clamming up is what the bad guys do. Following a self defense incident, you'll want to act like one of the good guys. You also won't want the investigating officers to miss any evidence or possible witnesses.
[4] Mas' recommendations (also reflected in the Jackson/Walters book) are:
* Say something like, "That person, or those people, attacked me." You are thus immediately planting the notion that you were the victim.
* Say something like, "I will sign a complaint." That establishes that you viewed the conduct of the other party to be criminal. It also shows a spirit of cooperation.
* Point out possible evidence, especially evidence that may not be immediate apparent. So if the assailant's knife slide under a car, tell the investigating officer. If the assailant dropped his gun in the bushes as he ran away, mention that. You don't want any such evidence to be missed.
* Point out possible witnesses.
* Then say something like, "Officer, you know how serious this is. I'm not going to say anything more right now. You'll have my full cooperation in 24 hours, after I've talked with my lawyer."
You will want to point out evidence, because you don't want the police to miss evidence that may be helpful to you. You want to point out witnesses, because if the witnesses are going to disagree with your story, the police are likely to find them anyway. You don't want to give the appearance of hiding anything. Your lawyer will deal with conflicts.