You’re an absolute fool to ever willingly cooperate with police, even in the investigation of a crime you know you had no involvement in. Even if lawyering up invites heightened suspicion, I say it’s worth the risk. And make sure it’s a lawyer versed in criminal prosecutions.

DNA evidence frees a man
who had done ten years in prison for a murder police say he committed
when he was 15. They pursued him for 12 years, won a conviction, then
kept in prison for a decade until the DNA evidence pointed to someone
else. The evidence against him seems to be that (1) the victim was
found in a park near his home, and (2) police found a series of violent
drawings in his home. It looks like his mistake was cooperating with
the police on the assumption that if he was innocent, he had nothing to
worry about by answering their questions.

And another one.

Note that in this case, Scott was convicted
largely because of a taped recording of him admitting to participating
in the crime. False confessions are much more common than you might
think. They happen for a variety of reasons (police brutality, the
desire to end a marathon interrogation, the belief that evidence will
surface proving innocence), but tend to occur most frequently with
young people (Scott was 15 at the time) and suspects with a low IQ or
mental handicap (Scott was learning disabled). In this case, Scott
appears to have been tricked into confessing by an investigator. What’s
unforgivable is that not only was there evidence exonerating Scott that
was never introduced at trial, but the DNA evidence could have been
tested years ago.

This is part of why I consider the police and the prosecutorial machine Public Enemy Number One, and that’s not hyperbole, nor am I unserious. I think you have far more chance of getting unjustly wrapped up in the system at some point in your life than you ever have of being assaulted by a stranger.