Upon dehydration, trehalose dihydrate transforms either toward a glassy amorphous state or toward a polymorphic crystalline phase depending on the dehydration protocol. Although this duality is now admitted, its origin remains an open question. We present here calorimetric and thermogravimetric experiments clearly showing that the main pertinent physical parameter governing this duality is the instantaneous rate of water release and not the thermal treatment used to dehydrate the sample. The latter, by acting on the rate of water loss, has only an indirect influence on the structure of the dehydrated product. A threshold rate of water removal, above which dehydration produces an amorphous state and below which it produces a polymorphic phase, is also defined.