There is no evidence of duct tape itself being poisonous to human beings. If burned, it may give off toxic fumes but there are no recorded cases of hospitalization due to this alone.
Vesta Stoudt invented duct tape during World War II as a way of protecting ammunition cases from water damage. It has a cotton fiber backing coated with waterproof polyethylene and a rubber based adhesive. Users nicknamed it "duck tape" due to the way water ran off it like a duck's back. After the war, it was frequently used to wrap air ducts, giving it the modern name of duct tape.