It depends on what is the relation between the dehydration temperature and the decomposition temperature of the dehydrated form. If they are separated well on the temperature scale, it is possible to distinguish the monohydrate from the anhydrous form. At the dehydration you will see an endotherm and a mass loss step. Do you have literature data on the two forms? It helps to design you experiment. You may also try to run DSC/TGA curves on samples heat treated in an oven around 100 deg C and compare it to the non heat treated sample.
I agree with my forewriters; a little bit more sophisticated is the usage of TGA coupled with FT-IR spectroscopy; the spectral informations of the evolved gases gives a clear insight what happens .
With DSC melting point for both forms will obviously be different, while any loss in weight during TGA analysis would only be observed in the monohydrate form.