Anyone (Jewish included) who does not wish to swear on a Bible to "tell the
truth, the whole truth, etc." may simply affirm to tell the truth, etc.
I guess you need only tell the judge/baliff beforehand "my client wishes
to affirm rather than swear".
I'm not sure of the halachic ramifications of swearing, but I can't imagine
that it's looked upon favorably to swear on a Christian bible. Besides,
Jewish law discourages swearing in God's name, lest one lies (even by
mistake) while under oath.
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