Unfortunately, the federal law that provides worker protection from the pseudoscience of polygraphy (the Employee Polygraph Protection Act of 1988) provides a categorical exemption to federal, state, and local governments. Thus, the relevant law will be your state's. In my home state of California, peace officers cannot be compelled to submit to lie detector testing. I believe that Illinois has a similar law. But you'll need to check your own state law and any administrative rules that might be applicable. If you are a member of a labor union, you can consult your union representative regarding your rights.

Your assessment that polygraphs are a crock is spot on. For a thorough debunking, see The Lie Behind the Lie Detector.

I'm not familiar with the applicable law in Virginia, but you might want to contact the Virginia Coalition of Police & Deputy Sheriffs, which has taken a public stance against polygraphy:

http://www.virginiacops.org/Articles/Polygraph/Polygraph.htm