Legal Question in Constitutional Law in California

I do not believe the judge would let the witness proceed until the witness answers "yes." If the witness refused to be sworn in she may be held in contempt of court. Even saying "no" once would seriously affect the witness' credibility.

Refusing to be sworn as a witness is contempt of court. If you have some issue with "swearing" or Bibles or "so help me God," just say so, and the court will be very happy to let you just promise to tell the truth.

A witness is required to testify truthfully. This requirement takes effect when he is subpoenaed or called to the stand, not when he takes the oath. The oath is a ceremony designed to ensure that he takes this requirement seriously. He is not free to say no, and he cannot evade the requirement for truthful testimony by doing so.

Saying no would indeed be contempt of court and would be dealt with accordingly. If you plan to do this, bring a toothbrush and some reading material. It will be a long time before you go home.