No one should ever take a polygraph because they aren't reliable, they are pseudoscience. Ask any lawyer they'll tell you refuse polygraphs no matter what, innocent or guilty don't touch them they do absolutely nothing for you, if LE believe you are involved or know something (even if you aren't) they aren't going to change their mind because you pass a polygraph it's not the 1960s LE are fully aware guilty people can pass polygraphs and innocent people can fail them which is why they aren't allowed in court. LE usually just offer you one to see if you're willing to take one and you shouldn't be under any circumstances.
Please don't believe someone is guilty based on them refusing a polygraph, polygraphs have played a major role in wrongful convictions and it's because there's a culture surrounding them where people believe if you refuse one you're guilty so people take them and if they fail or the polygraph turns up any signs of deception (which is very easy to do under the circumstances you take polygraphs since it monitors stress levels) LE uses it as a basis to build a case against the person that fails it. I don't think people are aware of how good certain prosecutors are at presenting flimsy circumstantial cases and how society inherently trusts them because they are authority figures meaning most juries are tainted before the trial even begins. Also that in America after conviction you need to produce new evidence for an appeal to be effective, disputing the evidence against you is not enough because you were convicted by a jury of your peers, meaning appeals are extremely difficult and your best shot is waiting decades until technology advances. Read about Kristine Bunch for example who was convicted of setting a fire that killed her kids she had to wait until arson investigation improved to prove she didn't do it, it was known by everyone following her case (including prosecutors since they used a witness they knew was lying) immediately that she was innocent yet she spent 16 years in prison because she couldn't produce new evidence, disputing the existing evidence wasn't enough.
Anyway, sorry i went on a tangent my point is please don't believe someone is guilty purely based on them refusing a polygraph, everyone should refuse them they should be abolished. I understand the logic behind believing it but doing so indirectly contributes to wrongful convictions. I'm not that familiar with this case so if there's other good reasons to suspect this person then fair enough but please do not factor polygraphs into your decision.