If you're not on their radar, being polite and forgettable is a great way to stay that way.
If you're already in custody, anything you say while being friendly can and will be used against you in court, so your vocabulary should probably be limited to the word "lawyer."
The problem starts when being polite and forgettable puts you on their radar. Police look in your backpack, and hey - it's a bike lock just like the one that was used to assault someone down the block a few minutes ago! You look about the right height. Which direction did you say you were coming from again?
Some situations can be lose-lose. Best you can do is don't talk to the police, and if you absolutely must, say as little as possible and don't lie.
If you're not on their radar, being polite and forgettable is a great way to stay that way.
If you're already in custody, anything you say while being friendly can and will be used against you in court, so your vocabulary should probably be limited to the word "lawyer."