Witnesses in North American court trials are sworn-in before testifying. They have historically been asked to promise to tell the truth "so help me God." This tradition has an ancient history, dating back to the late 18th century. ₁ At the time, the non-Native population of the U.S. was almost entirely Judeo-Christian and the vast majority of adults believed in a personal God and feared the possibility of being sentenced to an eternity in Hell if they angered God. By invoking God in the swearing-in ceremony, it was widely believed believed that witnesses would be less likely to commit perjury because of fear of angering God.
Belief in God has since become less common in North America; belief in a wrathful God who tortures people for all eternity in Hell is becoming rare except among religious conservatives. But the swearing-in tradition continues. Some state tax forms and other legal documents require the individual to swear truthfulness as well, upon penalty of a fine or jail sentence. ₂
The U.S. is generally regarded as the most religiously diverse country in the world. As the percentage of persons who identify themselves as Christians decreases, and the percentage of Agnostics, Atheists, those not associated with a religious faith, etc. increases, there have been efforts to remove references to the Judeo-Christian God from court rooms, government offices, public schools, etc. One of these changes has been to remove state-sponsored prayer from the schoolroom, while allowing students to pray on the school bus, around the flagpole, in school corridors, in religious clubs, over meals, etc. Another has been to drop the "so help me God" phrase in courtrooms. This has generated considerable distress among some devout people who interpret these changes as attacks on their religious heritage and religious freedoms.

One method of accommodation would be the policy of the Raytown court: to make the phrase optional. Atheists, Agnostics, Humanists, other non-theists, some Deists, etc. would then not be forced to imply a belief in the existence of a supreme being, which many would regard as a form of lying.Christians, Muslims, Jews and other theists can add the words "So help me God" if they personally wish follow tradition and make their belief in God publicNobody is forced to say something that they feel uncomfortable with. This is not a perfect solution, because there will still be some who would prefer that the phrase be compulsory and other who would wish that it be prohibited.Democracy does not necessarily mean that the majority should always rule. That often leads to the tyranny of the majority in which various minorities are oppressed. One of the functions of a constitution is to shield minorities from the wishes of the majority
http://www.religioustolerance.org/shmg.htm

This topic has come up more than once here at UM, do you think the majority should rule?
Always a pleasure
There are at least three different ways to handle the "So help me God" phrase:

We can proceed with the will of the majority which is definitely to retain the compulsory use of the phrase.
We can interpret the First Amendment of the U.S. Constitution as prohibiting government promotion of religion, and simply drop the phrase.
We can attempt to accommodate people's conflicting views by finding common ground -- some form of compromise.

There is a compromise already in the Constitution of the United States, that "oaths" of office may be sworn or "affirmed." Which, by the way, is an accommodation to those Christians who believe that secular oaths are contrary to scripture, as much as to non-believers.

Practice in law courts varies with jurisdiction. The key point, from the law's point of view, is that there be a "bright and shining line" between statements that expose the speaker to prosecution for perjury if they are false, versus other kinds of talk.

In any case, I do not see what "so help me God" adds to the ritual. Those who fear God's punishment would presumably be reluctant to lie, while those who do not fear God's wrath would as soon lie about that as about anything else. (Note careful phrasing: "would as soon" does not imply that those who do not fear God's wrath are more likely to lie than anybody else!).

Note added after a spell: We are so used to "so help me God" as a "formula" for oaths, that I think sometimes we forget that it is a prayer: Help me, God, to give good testimony. The state (at least in the United States) has no business telling its citizens to pray.