I am going to answer with my name and address. I am going to produce identification if requested. I am going to be polite, slightly formal, and as calm as I can be under the circumstances.
Where things get dicey is when the Police ask "What happened here?".
If I am a participant in the event, that is time to start with the scripted answers, which very quickly evolve to "I cannot answer any more questions until I have a chance to speak with my Lawyer".
Before the Lawyer talk shuts down the conversation:
If there were any visible weapons brandished by the other parties, I will mention that feature. If the other parties made aggressive and threatening moves toward me, I will mention that feature. If I sustained any injury, I will mention that feature, and I will also request medical attention. If I know there are other witnesses who "saw the whole thing", I will mention that feature, and try to describe those witnesses.
I won't discuss anything else, no matter how justified I think I might be. After being repeatedly pressed by the Police, it is time to end the conversation by bringing up the Lawyer.
Yes I am well aware that:
"Your silence and your refusal to answer questions that an innocent person might reasonably answer can be used against you in court until you have been Mirandized, or you have unequivocally asserted your right to silence." (Andrew F. Branca - The Law of Self-Defense, 3rd edition, pp 150)
Which is why the Lawyer needs to come out early in the interview stages.
And then I will stop talking.
Thanks - I had to look that one up.
https://www.nolo.com/legal-encyclopedia/when-how-invoke-your-right-silence.html