Also key: while you're talking with them, don't invite them inside. Talk to them outside, and if you do decide to talk with them to answer questions (ideally, with a lawyer), do it at a neutral location outside your home/office.
Definitely, whenever I have in the past talked to police officers (awesome parties ...) I always make sure to pull the door closed behind me. Then I am willing to have a chat. Usually it would come down to a "please keep the noise down, have a great evening" and we'd be set :-)
I guess I take this too far; I was staying in a friend's flat in Edinburgh; police showed up at the door, demanding entry -- I asked them for ID and then called the police to verify they were real cops, locked all my drives, etc., etc. Then after about 2-3 minutes, opened the door and went out into the hall -- turns out it was a gas leak. I'm sure they told stories about the paranoid American.
