What keeps people and society as a whole in check, the Bible or the law?

I think the best way to understand what keeps society in check is looking into statistical data.

While according to the study conducted by United Nations Office of Drug and Crime Japan has the least intentional homicide rate in the world, Denmark is the least corrupt one stated by the Transparency International.

The fact that neither Japanese nor Danish is society highly religious does not necessarily mean religion causes increase in crime rates or corruption in a country, however, based on these statistics we can safely conclude that for law and order or morality belief in Abrahamic God is not necessary.