The rule is different in criminal and civil cases. There is no inherent right against self-incrimination in a civil case, since you're not being accused of committing a crime and are not at risk of conviction.
You can plead the Fifth in a civil case if you believe that answering the question could subject you to criminal prosecution. But, unlike in a criminal case, where you have an absolute right to remain silent (and it can not be held against you), a judge or jury in a civil case can draw whatever conclusions they wish from your lack of testimony.
You can plead the Fifth in a civil case if you believe that answering the question could subject you to criminal prosecution. But, unlike in a criminal case, where you have an absolute right to remain silent (and it can not be held against you), a judge or jury in a civil case can draw whatever conclusions they wish from your lack of testimony.