if I were you I would certainly not take the polygraph, if you think you'll look guilty for not taking it, imagine what you'll look like if you lose the coinflip and fail the test, truthful or not. besides, if there was no damage done, what are you looking at? littering? You should definately read "the lie behind the lie detector", available on this forum, before even considering taking the polygraph.

8)

Sneeezermont,

I agree with George.  Under no circumstances should you submit to a polygraph test.

The fact is that if you "pass" the polygraph, there is no guarantee that suspicion will be removed.  And if you "fail," the results will be highly prejudicial.  Even if you tell the truth, how the "test" will turn out is a crap shoot due to the unreliability of the polygraph.  Most importantly, any agreement to be polygraphed by the police is an agreement to sit down with an expert interrogator, with no attorney present !  This is simply not an intelligent decision.

You are basically stuck between a rock and a hard place.  On one hand, you want to cooperate with the police and appear that you have nothing to hide.  On the other hand, it is absolutely not in your best interest to submit to this “test.”  You would be wise to choose the lesser of the two evils, which is to refuse this “test.” Once again, like George said, you are already a suspect.  Do not allow the police to circumvent your right to remain silent simply because they claim to have an imaginary device that can determine truth from deception that they claim will help clear you if you tell the truth is simply unwise.  I suggest simply once again stating that you had nothing to do with the incident.  If they actually arrest you, remain silent and get a laywer.  

You can take solace in two major facts.  First, you can bet that a vast majority of police officers themselves, if called by a family member in your situation requesting advice, would tell the person not submit to a police polygraph under any circumstances.  The same goes for competent defense attorneys.   Second, the polygraph is most often used in situations where the police have little to no evidence against a suspect (you) and thus have little chance of a successful prosecution without a confession.  

Like George said, tell the police that you know that the polygraph has never been proven by peer-reviewed scientific research to operate at better than chance levels of accuracy, and that you are refusing for this reason.  They may act like your refusal makes you “look guilty”—but in actuality, the police know that any rational person who knows the truth about the polygraph would make this decision.  Personally, I would rather choose the lesser evil and run the risk of “looking guilty” rather than chance having a false confession (which could later  be used in court) attributed to me.