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For criminal matters, the short answer is, never. See Don't Talk to the Police. [1]. You want a defense attorney to handle this.

For civil matters, although IANAL I think similar reasons apply, so similar answer: Don't Talk to the Public. If you're truly famous enough to need to break this rule, then you need an attorney who specializes in high-profile cases like this.

Edit: By "cases like this", I mean an actor or athlete level of celebrity. Probably not John Carmack, despite how famous and awesome he may be within our circles. Really, the smartest thing is to just "shut up". Even though a false accusation is a genuine personal violation and you want to defend yourself, the best defense usually won't be DIY.

[1] https://www.youtube.com/watch?v=6wXkI4t7nuc