If you are completely innocent, my advice would be to submit to polygraph testing. The odds favor that you will pass the test and be eliminated as a suspect in the criminal case. If for some reason you fail the polygraph test, the results are inadmissible in court. If you are involved in any way with the criminal case, you should refuse to submit to polygraph testing and assert your constitutional right to remain silent. The police are only interested in obtaining convictions and are highly trained in the fine art of securing confessions from potential suspects. Don't give them the opportunity.
Before making a decision on whether or not to submit to polygraph testing, your case needs to be reviewed by an experienced criminal defense attorney. Contact attorney Robert J. Shane at (612) 339-1024 for a free phone consultation or visit his website for more information at http://www.criminallawyerminnesota.com