I believe that Ayoob's recommendation for a statement is more reasonable and less likely to get you into more trouble. This synopsis is the way I remember it, it is not exact:
"Officer, that man attacked me; I will sign a complaint."
"There are witnesses; there is evidence."
"Officer, I am willing to answer additional questions as soon as I have consulted with my attorney."
The first statement(s) establish you as the victim. The second statement(s) do what you can to make sure evidence is collected. Do NOT expect them to do a complete sweep or cordon anything off or call in a forensics team. You need to tell them where stuff is, especially if the encounter/fight covered any distance whatsoever between start and finish. The last statement tells them you'll not be saying anything else until you have the attorney present.
One other thing: This kind of statement, whichever one you make and in whichever form you make it, needs to be rehearsed and practiced like anything else. You should be running the initial phone call you make to the PD, your actions as they arrive, and the statements you make, though your mind from time to time, and consider walking through them at the range on occasion after you run a drill.