You give the police one story when they first question you. Then they confront you with various pieces of evidence they've already obtained, and then you tell them a different story.
The second story's usually just as unpersuasive -- indeed, often even more so -- than the first one. And typically just incriminates you even more.
Here, for example.
Just be quiet. You're not going to help yourself. Just the opposite.
Better yet, don't commit the murder in the first place.
