Ferromagnetic (FM)/heavy metal (HM) nanostructures can be used for the magnetic state readout in the proposed magneto-electric spin-orbit logic by locally injecting a spin-polarized current and measure the spin-to-charge conversion via the spin Hall effect. However, this local configuration is prone to spurious signals. In this work, we address spurious Hall effects that can contaminate the spin Hall signal in these FM/HM T-shaped nanostructures. The most pronounced Hall effects in our Co50Fe50/Pt nanostructures are the planar Hall effect and the anomalous Hall effect generated in the FM nanowire. We find that the planar Hall effect, induced by misalignment between magnetization and current direction in the FM wire, is manifested as a shift in the measured baseline resistance, but does not alter the spin Hall signal. In contrast, the anomalous Hall effect, arising from the charge current distribution within the FM, adds to the spin Hall signal. However, the effect can be made insignificant by minimizing the shunting effect via proper design of the device. We conclude that local spin injection in FM/HM nanostructures is a suitable tool for measuring spin Hall signals and, therefore, a valid method for magnetic state readout in prospective spin-based logic.