I have never heard of carvings and hieroglyphics on the back of the statues
The message got carved on any convenient surface, like these cool block statues popular during the 18th Dynasty; this one portrays Senenmut, lover and architect of the chick pharaoh Hatshepsut, shown here with their daughter Neferure.
http://www.touregypt.net/featurestories/cachette9.htm
There are other examples of these two, not in block form. There’s also this one of Senenmut by himself, in the block form: