  In this contribution, we summarize our results concerning the observational
constraints on the electric charge associated with the Galactic centre black
hole - Sgr A*. According to the no-hair theorem, every astrophysical black
hole, including supermassive black holes, is characterized by at most three
classical, externally observable parameters - mass, spin, and the electric
charge. While the mass and the spin have routinely been measured by several
methods, the electric charge has usually been neglected, based on the arguments
of efficient discharge in astrophysical plasmas. From a theoretical point of
view, the black hole can attain charge due to the mass imbalance between
protons and electrons in fully ionized plasmas, which yields about $\sim
10^8\,{\rm C}$ for Sgr A*. The second, induction mechanism concerns rotating
Kerr black holes embedded in an external magnetic field, which leads to
electric field generation due to the twisting of magnetic field lines. This
electric field can be associated with the induced Wald charge, for which we
calculate the upper limit of $\sim 10^{15}\,{\rm C}$ for Sgr A*. Although the
maximum theoretical limit of $\sim 10^{15}\,{\rm C}$ is still 12 orders of
magnitude smaller than the extremal charge of Sgr A*, we analyse a few
astrophysical consequences of having a black hole with a small charge in the
Galactic centre. Two most prominent ones are the effect on the X-ray
bremsstrahlung profile and the effect on the position of the innermost stable
circular orbit.
