If I am innocent, shouldn't I make a statement and tell the police everything I know?

Absolutely not.

When a person is innocent or has a valid defense such as self defense, it is common to want to explain your side of the story to police. However, even if you are innocent it is crucial that you nevertheless invoke your right to an attorney and your right to remain silent. According to the Innocence Project, defendants confessed or admitted guilt in about 25% of cases where people served time in prison for crimes that they didn't commit.

For more information on confessing to crimes you did not commit despite actual innocence, see Frontline's "The Confessions" and innocenceproject.org.

Especially if you are innocent, you should always invoke your right to counsel and right to remain silent and get an attorney immediately.