Topological insulators provide a new platform for spintronics due to the spin texture of the surface states that are topologically robust against elastic backscattering. Here, we report on an investigation of the measured voltage obtained from efforts to electrically probe spin-momentum locking in the topological insulator Bi$_2$Se$_3$ using ferromagnetic contacts. Upon inverting the magnetization of the ferromagnetic contacts, we find a reversal of the measured voltage. Extensive analysis of the bias and temperature dependence of this voltage was done, considering the orientation of the magnetization relative to the current. Our findings indicate that the measured voltage can arise due to fringe-field-induced Hall voltages, different from current-induced spin polarization of the surface state charge carriers, as reported recently. Understanding the nontrivial origin of the measured voltage is important for realizing spintronic devices with topological insulators.