There are circumstances where refusing to answer questions when subpoeaned to court could result in your incarceration. For example, you cannot plead the Fifth if the answer will not incriminate you or if the court has granted you immunity from prosecution. There are many different possibilities and I would encourage you to speak with an attorney.
I would like to add to the prior answer in clarifying what pleading the fifth is and what privilege it protects. The 5th Amendment to the Constitution of the United States says in relevant part, "No person shall be compelled in any criminal case to be a witness against himself..". This means that you may plead the fifth only if your testimony could be used to prosecute you for what your testimony may reveal. You cannot plead the fifth to protect another person, and further one cannot make the plea if there are only civil penalties (most civil liability has a criminal analog). One may plead the fifth in a civil case if that testimony reveals an admission of guilt to criminal activity. If a witness attempts to plead the fifth improperly and for improper reasons, then that person may be held in contempt of court.