  Using the Keldysh nonequilibrium Green function technique, we study the
current and shot noise spectroscopy of a single molecular quantum dot coupled
to a local phonon mode. It is found that in the presence of electron-phonon
coupling, in addition to the resonant peak associated with the single level of
the dot, satellite peaks with the separation set by the frequency of phonon
mode appear in the differential conductance. In the ``single level'' resonant
tunneling region, the differential shot noise power exhibit two split peaks.
However, only single peaks show up in the ``phonon assisted''
resonant-tunneling region. An experimental setup to test these predictions is
also proposed.
