Why you should not talk to the police:
The United States Supreme Court (SCOTUS) has repeatedly held that police can lie to you during their investigations and there is no remedy for their deception. The prosecutor can use all the evidence the police gather by lying, and there isn't a thing you can do about it.
So, remember these Basic Rules.
1) DO NOT TALK TO THE POLICE
2) DO NOT TALK TO THE POLICE
3) DO NOT TALK TO THE POLICE
4) See, rules 1-3, above.
5) Call a lawyer you can trust, and call immediately.
The best time to call a lawyer is before you are charged! If you get even a hint that you are under investigation, don't talk to anyone other than a skilled criminal defense lawyer.