A very straight reading of Matthew and James would lead you to believe what Jeff wrote. But that may not be the end of it, or have anything to do at all with judicial oaths.
Christ meant, as the Fathers and ecclesiastical writers explain, to be so truthful that men could believe them without need of oath to confirm what they say. He did not forbid the use of oaths under proper conditions, when necessary to satisfy others of our truthfulness.
Oaths - Catholic Encylopedia
All the sacraments are oaths. Saying Amen is an oath. Every covenant God made is an oath. There's no reason you shouldn't "swear to God" when you're seriously "swearing to God". Just like you can say "God help us" or "Mother of the Saints!" without using God's name or other holy names in vain.
You shouldn't go down a path that is going to lead to perjury.
However, swearing on a Bible, or swearing on "The Precious" or your mother's ashes, etc doesn't seem necessary does it? Almost seems idolatrous. But, then again, you're not swearing on a Bible, you're just touching a Bible and swearing on the Holy Word of God and as long as you're not perjuring yourself and you're fulfilling your obligations, you're doing the right thing.