We have studied the generation of surface charge distributions on polymer surfaces due to the deposition, motion and evaporation of liquid droplets. Using liquids with different static dielectric constants, we found that the magnitude of the surface charge conforms well to the Boltzmann relation for the dissociation probability of ions in solution, indicating that the phenomenon is electrokinetic in nature. The origin of the sensitive dependence of the surface charge on the substrate thickness was identified to be an image charge effect. Experiments on polycarbonate and chemically-amplified photoresist yield surface charges of opposite polarity. By varying the photoresist composition, we identified the leaching of negative quencher ions as the reason for the charge inversion.