Schottky CdTe X-ray detectors exhibit excellent spectroscopic performance but suffer from instabilities. Hence it is of extreme relevance to investigate their electrical properties. A systematic study of the electric field distribution and the current flowing in such detectors under optical perturbations is presented here. The detector response is explored by varying experimental parameters, such as voltage, temperature, and radiation wavelength. The strongest perturbation is observed under 850 nm irradiation, bulk carrier recombination becoming effective there. Cathode and anode irradiations evidence the crucial role of the contacts, the cathode being Ohmic and the anode blocking. In particular, under irradiation of the cathode, charge injection occurs and peculiar kinks, typical of trap filling, are observed both in the current-voltage characteristic and during transients. The simultaneous access to the electric field and the current highlights the correlation between free and fixed charges, and unveils carrier transport/collection mechanisms otherwise hidden.