  The recently released images of the supermassive black holes in the M87
galaxy and the galaxy of our own make probing black hole spacetimes and testing
general relativity (GR) possible. The violation of equatorial reflection
symmetry of black hole spacetimes is clearly a smoking gun of physics beyond
GR. In this paper, we place constraints on the violation of black hole
reflection symmetry using the bounds on the ring size of the Sgr A* black hole
images, which are consistent with the critical curve radius predicted in GR
within $\sim10\%$. Adopting a theory-agnostic framework, we consider a
Kerr-like metric in which the violation of reflection symmetry is parametrized
by a single parameter, without altering the multipoles of the black hole. The
critical curves are always vertically symmetric due to the existence of hidden
symmetry associated with the Killing tensor, even though the spacetime is
reflection asymmetric. We find that the size of critical curves is sensitive to
the amount of reflection symmetry being violated, and place the first
constraints on the parameter space of the model using the Sgr A* images.
