A suspect cannot be made to give evidence against themselves. In fact, they cannot be made to even speak with the police; they are under no obligation to do so. This is true even if the police show up to their house. Accordingly you need not submit to a polygraph or any other questioning whatsoever. At this point, you should not have any more contact with the authorities without having first consulted directly with a local criminal law attorney. They can best advise you further.
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