A further 12-month trial is expected to start in April, the force says.
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Acpo, which represents chief police officers in England, Wales and Northern Ireland, said its Homicide Working Group advised police on the use of polygraph techniques.
"Polygraph techniques are complex and are by no means a single solution to solving crimes, potentially offering in certain circumstances an additional tool to structured interrogation," a spokeswoman said.
"These initial trials are in their very early stages and we will follow their progress, working with chief officers across the country to provide further guidance if necessary.
"Whether these techniques are adopted elsewhere in the country is a matter for individual chief constables."
The results of lie detector tests are considered too unreliable for use in criminal trials.
Bruce Burgess, a former chairman of the British Polygraph Association, said lie detectors were considered to be a useful "investigative tool" in the US, even though they produced evidence that was "very difficult to get into court" and were unlikely ever to be used as "a guilty or innocent tool".
He said offering polygraph tests to a number of suspects could provide a degree of insight if, for example, somebody refused to take the test.
"If they polygraph six people and they get five truthful results and one deceptive, they can home in on that person and cut down on a lot of police work. That's the way it's used in America," he added.
Although the Hertfordshire pilot looked at the use of lie detectors to aid decisions over whether or not to charge suspects, a three-year pilot study in the East and West Midlands could lead to the compulsory testing of convicted sex offenders."
