The Galactic centre supermassive black hole (SMBH), in sharp contrast with its complex environment, is characterized by only three classical parameters - mass, spin, and electric charge. Its charge is poorly constrained. It is, however, usually assumed to be zero because of neutralization due to the presence of plasma. We revisit the question of the SMBII charge and put realistic limits on its value, time-scales of charging and discharging, and observable consequences of the potential, small charge associated with the Galactic centre black hole. The electric charge due to classical arguments based on the mass difference between protons and electrons is less than or similar to 10^9 C and is of a transient nature on the viscous time-scale. However, the rotation of a black hole in magnetic field generates electric field due to the twisting of magnetic field lines. This electric field can be associated with induced charge, for which we estimate an upper limit of less than or similar to 10^{15} C. Moreover, this charge is most likely positive due to an expected alignment between the magnetic field and the black hole spin. Even a small charge of this order significantly shifts the position of the innermost stable circular orbit (ISCO) of charged particles. In addition, we propose a novel observational test based on the presence of the bremsstrahlung surface brightness decrease, which is more sensitive for smaller unshielded electric charges than the black hole shadow size. Based on this test, the current upper observational limit on the charge of Sgr A* is less than or similar to 3 x 10^8 C.