If you are talking about the political and legal system of the United States, the judicial branch has only a very small role to play in the process of impeachment. Impeachment is, instead, largely something that is done by Congress. The only real role that the judicial branch has in the proceedings is that the Chief Justice of the Supreme Court of the United States presides at the trial if the president is the one being impeached. Otherwise, the judicial branch has no role.
Members of the judicial branch themselves can be impeached, however. That is the other way in which impeachment is tied to the judicial branch.