The thing is, lie detector operators don't say "Did you murder him?" They first ask simple questions to see what the person does when they lie ("Have you ever stolen?" is a good one because practically nobody hasn't) and then they ask questions like "Do you know this person?"
But the thing is, some people may not believe they broke the law because they think the murder was justified. Or, alternately, they may not remember the whole thing because they were on drugs. The only reliable lie detector in my opinion is the brain scan. Of course, that's way more expensive.