Although the First Amendment of the U.S. Constitution declares:
"Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances."
Christian Bibles are sometimes used in Courts to swear an oath.
In contrast to the tradition of swearing by the Bible, we are told in Matthew 5:33-37:
 “Again, you have heard that it was said to the people long ago, ‘Do not break your oath, but fulfill to the Lord the vows you have made.’  But I tell you, do not swear an oath at all: either by heaven, for it is God’s throne;  or by the earth, for it is his footstool; or by Jerusalem, for it is the city of the Great King.  And do not swear by your head, for you cannot make even one hair white or black.  All you need to say is simply ‘Yes’ or ‘No’; anything beyond this comes from the evil one."
If Matthew 5:33-37 is literal, why would Christians swear an oath on the Bible?