This [1]
is an engaging and fascinating video presentation by Professor James
Duane of the Regent University School of Law, explaining why -- in a
criminal matter -- you should never, ever, ever talk to the police or
any other government agent. It doesn't matter if you're guilty or
innocent, if you have an alibi or not -- it isn't possible for anything
you say to help you, and it's very possible that innocuous things you
say will hurt you.

Definitely worth half an hour of your time.

And this [2] is a video of Virginia Beach Police Department Officer George Bruch, who basically says that Duane is right.