Polygraphs are not admissible as evidence, nor is refusal to submit to one. They can be requested in interrogations if you agree, you may well be lied to about the results in an attempt to get a confession. You should never agree to take one if you find yourself in this circumstance.
But, last I checked, polygraphs were required for certain government positions in the U.S, but am having a problem finding a citation for that right now.
Ah, yes. I was speaking only in the context of a criminal investigation/prosecution. The page you linked states: While polygraph tests are commonly used in police investigations in the US, no defendant or witness can be forced to undergo the test
It appears some states may allow the results to be presented, but sounds like it cannot be required.