In most cases, no. Remember, you are presumed INNOCENT. You are not required to prove anything. You are not going to convince the police not to charge you. They won't believe you even if you pass the lie detector test. Be happy they asked you to take a polygraph — it usually means they don't have enough evidence and they are fishing for a confession. Also, remember that polygraph tests are not admissible at trial — not even if you pass.
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