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Thin-film-on-ASIC (TFA) detectors are monolithic pixel devices that consist of amorphous silicon detecting diodes directly deposited on readout electronics. This paper presents a characterization of the TFA spatial resolution using the electron-beam-induced current (EBIC) technique, in which pixel pads patterned in microstrips were swept by the beam. We measured the spatial resolution for different configurations and thicknesses of the TFA active layer with different beam energies, currents and sweep speeds. We observed that the generated electron-hole pairs are collected most efficiently when the beam is over the microstrips. This better collection efficiency gives a larger signal than off the strips, and thereby enabled us to distinguish strips as small as 0.6 μm wide which are spaced by 1.4 μm gaps. This high spatial resolution was obtained even though microvoids in the amorphous silicon layer-induced by an ASIC morphology as rough as 2 μm-were observed in the detector cross section, thus demonstrating the potential of the TFA architecture even with non-planar readout electronics.