Requirement for Polygraph test in employment

Taylor is applying for a position as a teller at First Bank and Trust Company of Tinseltown. He submits a resume and attends an interview with the human resources department and, a few days later, gets a call from the human resources department telling him that he has moved to the next level of consideration that involves him taking a polygraph test. Does the requirement that Taylor take a polygraph test to be further considered for this position violate any law? Why, or why not? What law is involved?