In most countries the police does an independent investigation, and what you say to them can also be used in your defense. The police can be called to testify

In most countries the police does an independent investigation, and what you say to them can also be used in your defense. The police can be called to testify on your behalf; just as well as they can testify against you. Not always a reason to talk, but it makes it less dangerous to help the police. After all we do want to help the police catch criminals don't we?