While there are some people and some organizations that believe in the validity of lie detector tests, in point of fact, lie detector tests (aka polygraph tests) as currently structured, don't really measure whether someone is or is not lying, but functionally measure their anxiety levels which is not the same thing. Additionally, the Supreme Court has ruled that courts under federal jurisdiction, that lie detector tests are not admissible, and in the States that do permit lie detector tests, these are usually constructed in a manner in which both the prosecution and the defense have come to terms in regards to how, who, and what will or will not be performed in order to properly administered the lie detector test, and the results so concluded.
Unfortunately, the average citizen really doesn't know what is or isn't admissible in regards to a lie detector test and further often don't seem to know their Constitutional rights, in regards to such a test, of which no suspect so arrested is required to take such a test, and should especially be wary of taking such a test, if the test is administered and monitored by police officials, as opposed to being conducted through an independent and audited company. Not only that, most citizens are unaware that police are permitted to deliberately lie to suspects, about, just about everything in regards to a case. Police can lie about DNA results, they can lie about lie detector results, they can lie about physical evidence, and they can pretty much lie about any and everything, as long as such deceit does not cross the line where it is reasonably likely to produce a false confession. No doubt, that line is seldom breached.
So then, suspects that are arrested, especially those that are arrested having not committed the crime in question, should seldom, if ever, be eager to take a lie detector test, unless advised to do so by counsel, and only under the conditions as instructed by that counsel; for police officers far too often, have every advantage of trickery, deceit, and deception on their side, which they are not reluctant to utilize and to employ so as to procure convictions, and don't seem to readily care whether such a confession leading to the conviction is actually legitimate or not, though, of course, there are some fine officers that actually do respect and uphold Constitutional law.
The point of it all, is once that a person is arrested, those that have been arrested and are now being questioned or interrogated, are in virtually every case, in a situation, in which the officer(s) so doing the interrogation isn't interested in the truth, per se, because they aren't actually listening for the truth, but instead, would prefer to trip the suspect up; and regrettably will often resort to lying, dishonesty, and duplicity to get whatever actionable information that they can from the suspect. What is somewhat ironic is that the police officer often claims that they are after the truth, and therefore that the suspect should tell the officer nothing but the truth and the whole truth, whereas on the other hand, the police officer is typically doing none of the truth telling on their part.
Any legal system that countenances lying and deceit from the officials that are part and parcel of that justice system, of which, those officials have an inherent duty to uphold the law, and to thereby conduct themselves faithfully to that duty, is in actuality a justice system in name only, but not in function or actuality.