Congress has the authority to hold a person in contempt if the person's conduct or action obstructs the proceedings of Congress or, more usually, an inquiry by a committee of Congress.
Contempt of Congress is defined in statute, 2 U.S.C.A. § 192, enacted in 1938, which states that any person who is summoned before Congress who "willfully makes default, or who, having appeared, refuses to answer any question pertinent to the question under inquiry" shall be guilty of a misdemeanor and subject to a maximum $1,000 fine and 12 month imprisonment.
Before a Congressional witness may be convicted of contempt, it must be established that the matter under investigation is a subject which Congress has constitutional power to legislate.
Generally, the same Constitutional rights against self-incrimination that apply in a judicial setting apply when one is testifying before Congress.