The police think I committed a robbery and want me to take a polygraph test at the police station. Should I do that?

ABSOLUTELY NOT. The worst thing you could ever do when being accused of a crime is voluntarily show up at the police department and speak to anyone. You should never, ever, ever speak to law enforcement if you are being suspected of a crime. Worse yet, you should never agree to take a polygraph at any police station. The police officers who work the polygraph machines are trained to obtain a confession from you after telling you that you failed the polygraph test (whether you failed or passed). If you are being accused of a crime immediately contact a lawyer.