Yes, but only under certain circumstances. One more detail:
Suppose a prosecutor hauls you before a grand jury investigating the criminal activities of your father, brother, cousin, etc. You could "plead the Fifth": claim that if you answered questions about your father's criminal activities, your answers would incriminate you because you were a partner, witness, etc. The judge then could offer you "immunity to testify": that is, he could say to you that you will not be prosecuted for any crimes you admit to while testifying, in return for answering all questions about your father truthfully. If you still refused, you could be held in contempt of court. You see, the Fifth Amendment protects you against incriminating yourself. But if a judge guarantees that you won't be prosecuted if you testify, the law assumes that you no longer need that protection--hence, you can be held in contempt of court if you refuse.