MagicStarER,
You have the option to refuse the polygraph, and you should exercise that option. You also have the option to refuse to be interrogated without a lawyer present, and you should also exercise this option.
As used by law enforcement agencies in criminal investigations, polygraph "testing" is often little more than a pretext for interrogating a suspect without a lawyer present. Sometimes the "test" is even rigged: regardless of what the charts might suggest (not that polygraphy has any validity to begin with), the suspect is told that he has failed and subjected to an interrogation. It is not unprecedented for innocent persons, confronted with having (wrongly) "failed" a polygraph, to become mispersuaded that their best option is to make a false confession.
The fact that you have been previously subjected to harsh interrogation regarding the relevant issues, and that the investigators wish to take you to a distant, unfamiliar setting, where you will not feel free to end the interrogation at will (presumably being dependent on the detectives for transportation home) does not bode well at all.
Also, you need to understand that polygraph "testing" has no scientific basis whatsoever. It's sheer quackery, in the same league as phrenology and graphology.See our e-book,
The Lie Behind the Lie Detector for an exposé of the kinds of trickery you can expect to encounter should you (against my advice) agree to this "test":
http://antipolygraph.org/lie-behind-the-lie-detector.pdf I agree with "someone" that you need a lawyer. And you would be wise not to speak with investigators again without your lawyer present. If you don't already have a lawyer, Martindale's on-line Lawyer Locator might be helpful in finding one near you:
http://www.martindale.com In addition to posting via this message board, please feel free to e-mail or call me.