We measured the complex conductivity of carbon nanotube-polypropylene composites under mechanical shear conditions. In order to determine how flow alters the properties of these complex fluids we constructed a rheo-dielectric test fixture, which allows for the simultaneous in situ measurement of both the frequency dependent complex electrical conductivity and basic theological properties, such as shearing rate, viscosity, normal stresses. We analyzed the results using Generalized Effective Medium theory. The scaled conductivity of percolated networks compares well with the universal trend showing a power law scaling with frequency. We find that the conductivity percolation concentration (phi(c)) increases with increasing shear rate. For sufficiently high shear rates, the nanocomposite undergoes a transition from a conducting to an insulating state. The shear rate dependence of phi(c), which gives rise to this transition, conforms well to a model that we introduced to describe this effect.