You are a public employee; therefore, you have certain benefits and protections that most corporate employees do not have. You need to find out if your collective bargaining agreement/union opposes this and/or knows about it or if the agreement itself prohibits this practice. It sounds fishy and I would not submit to a lie detector test if one is not needed for disciplinary purposes or job promotion purposes. You need to consult personnel for this matter and then possibly speak witb your union representative or private counsel about this mandate.