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The observation of zero electric field level crossing, the electric analog of the Hanle effect, permits the measurement of electric dipole moments in excited electronic states. We have applied this technique to the Clements E band of $SO2$. A free jet expansion of $SO2$ seeded in argon was crossed with the output of a doubled, Nd:YAG pumped, dye laser. $SO2$ fluorescence was collected along the third orthogonal direction. The electric field was established by two transparent electrodes located above and below the plane defined by the molecular beam and the laser beam. The laser was polarized parallel to the external field. The electric field was applied during alternate laser pulses, and the boxcar integrator used to process the photomultiplier output averaged the difference between the fluorescence intensity with and without the field. Initial data were obtained for the Clements E band. The laser frequency was fixed at the $110\leftarrow 000$ excitation, so only fluorescence from the $110,M=0$ state was detected in strong field conditions. As the electric field was reduced, the Stark splitting between the $110.M=0$ and the $110,M=\pm 1$ levels first became comparable to the homogeneous linewidth and then the detected fluorescence approached the zero field value. The electric field corresponding to the half height of this level crossing signal was observed to be 138v/cm. Using this value, and the known radiative lifetime, produced an excited state dipole moment of 0.76 D.