I want to know whether applicants have ever been fired or stolen from a prior employer — can I require them to take a lie detector test?
No. A federal law called the Employee Polygraph Protection Act (and the laws of many states) prohibits almost all employers from asking or requiring applicants to take a lie detector test. The only exception is for employers that deal in controlled substances or provide certain types of security services, who are allowed to require certain applicants to take a polygraph test (a particular kind of lie detector test).
