Back in the day a person could not be a witness if s/he was an atheist. By being G_d fearing, a person would be frightened of not telling the truth. The courts would make the witnesses swear upon the Bible to impress upon both the seriousness and their desire to show that if the witness would lie, s/he would pay for it in the afterlife. That is the reason why atheists were not allowed to speak in court, no fear to them of eternal damnation.
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Basically, the reasoning is to try and make everyone tell the truth. I actually had to swear on one just to go through the jury selection process (which I got out of successfully, by the way). There isn't really any legal precedence for it as much as there is simple tradition. I believe oaths have been used in courtrooms for centuries, and oaths in general go back to before Christ (B.C.).
Source(s):
http://en.wikipedia.org/wiki/Oath

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