In my Bad Self days, I was stopped and/or detained by the police for questioning more than once. I'd had dinned into me the mantra Give them nothing but I always found myself beginning to talk; I wanted, on some level, to be liked. I wanted to be a Good Detainee; I wanted them to understand I was a nice girl in terrible circumstances. (I wanted the world to be a reasonable place.) I always managed to shut myself up eventually, but, oh, the impulse was there.
Here's a video that explains better than I ever could why it's a bad idea, a very very bad idea, even if you're the most super innocent on the planet, to say anything to police if they want to ask you a few questions in connection with a crime. It's a 25-minute argument by a law professor for pleading the fifth.
Law enforcement people are not kidding when they say 'anything you say may be used in evidence against you'. Anything. And here's the kicker: nothing you say may be used in evidence for you, because then it becomes hearsay. The lawyer here talks too fast, and he's just a wee bit smug, but the information he delivers is excellent. I recommend that you watch it.
If for some reason you can't see the video, follow this link instead. (Thanks, Cindy.)