Your father should not take the polygraph. It's a pseudoscientific fraud that is inherently biased against the truthful. Moreover, because investigators do not believe your father's account, his "failing" may be part of the interrogation plan. Post-test interrogations can be highly manipulative and/or coercive, and innocent people have ended up going to jail after making false confessions.

For a thorough exposition of polygraphy and the trickery and deceit on which it depends, see our book, The Lie Behind the Lie Detector, which you can download here:

https://antipolygraph.org/lie-behind-the-lie-detector.pdf

Moreover, your father should fire his attorney, whose advice that he consent to a lie detector "test" is tantamount to malpractice.

so here's the story
my father recently had a fire, it was an accident and he admits to it. the firemarshall and police say they dont believe his story and are asking him to take a polygragh test. 
he has been in horrible shape ever since the fire. he hasnt been eating and is just killing himself that he let such a thing happen and now that they are accusing him of starting the fire and want him to take the test he is even more nervous. he's constantly shakey pale and stuttery. 

my question is should he take the test or tell them to shuv it? his attorney says dont worry go ahead and take it but with as nervous as he is im afraid he's going to false positive like crazy.

they are telling him that it is not going to be a deciding factor in the investigation. are they lieing to him?

thanks for any help u guys can give this is a very hard time and this damn test is making it nearly unbearable