During his first swearing in, Obama did it with the bible used by Abraham Lincoln, as a way of commemorating the 150th anniversary of Lincoln’s Emancipation Proclamation. In his second inauguration two months ago, BO used the “traveling” Bible of Martin Luther King Jr, as a way of celebrating the 50th anniversary of the March on Washington (Led by Dr. King).
I do not think there is a constitutional requirement on how to hold or not hold the bible, or even a requirement to use one at all! Theodore Roosevelt in 1925 used none!
In the case of Uhuru Kenyatta having the first lady hold the bible for him as he is sworn in (Obama does it), I think he wants to offer a glimpse into his spiritual life or at least, into how he wants his spiritual life to be understood-that it starts and is deeply rooted in the family.
It would however, be interesting to see which verse Uhuru will choose to signify his day. In the face of divisions in the country, maybe he could borrow a leaf from Ronald Reagan, who would be sworn to the passage in the bible that says: “If my people, which are called by my name, shall humble themselves, and pray, and seek my face, and turn from their wicked ways; then will I hear from heaven, and will forgive their sin, and will heal their land”.