If an employer puts it in the work contract that they may require a polygraph (either to gain employment or keep it) can I refuse?
The relevant statutory body regarding polygraphs in the US mentions on their website that nobody can be forced to do a polygraph. It also mentions refusing to do one is not an admission of guilt.
It depends. There is a law, 29 USC Ch. 22, which generally prohibits employers from requiring polygraph tests before or during employment. However, there are exceptions. It only limits private employers, not governments; certain private employers are allowed to require such tests. The exemptions are set out here. They broadly fall into "government security concerns" (defense subcontractors etc.), security firms, and drug companies.
The penalties to be visited on violators are spelled out here.
