The accuracy rates are disputed, but almost certainly the controlled question test does have higher than chance accuracy at finding a true positive. However, it also has a fairly high risk of a false positive, possibly as high as 25-27%. Polygraph proponents claim that the accuracy can be 90% or higher but this is likely to be wildly exaggerated and based on selective reporting. Some studies find around 60-70%.
Field studies are difficult to conduct and lab studies have poor external validity. I was just saw a
recent review but haven't had time to read it in detail.
I suspect that using it to monitor offenders is partly a bogus pipeline procedure to scare people into thinking they'll get caught.
A forensic psychology text says that false negatives are less likely than false positives, ranging 1-13% across studies.