From my POV, cops tend to ignore anything that doesn't point to "guilty". There would be no benefit to the accused in this case. IANAL, yada, yada.
What about if you are wanted for questioning about a murder which involved dragging the body a significant distance while you were in the hospital recovering from chemotherapy? Still don't talk to the cops?
Nope. While you're busy playing "what if...", I'm dialing a lawyer. Should that trained professional advise talking to the adversarial trained professionals, then I would do so, and not before.
I don't how it is where you're at, but in the U. S. cops have demonstrated time and again (and I've seen with my own eyes) that they are not concerned about truth and justice, but arrest and conviction rates. I'm not walking into that scenario running my mouth without professional advice.