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We study a viable connection between the circular-equatorial orbits andreflection symmetry across the equatorial plane of a vacuum stationaryaxis-symmetric spacetime in general relativity. The behavior of the circularequatorial orbits in the direction perpendicular to the equatorial plane isstudied, and different outcomes in the presence and in the absence of thereflection symmetry are discussed. We conclude that in the absence of theequatorial reflection symmetry neither stable nor unstable circular orbit canexist on the equatorial plane. Moreover, to address the observational aspects,we provide two possible examples relating gravitational wave astronomy and thethin accretion disk which can put constraints on the symmetry breakingparameters.

Possible connection between the reflection symmetry and existence of equatorial circular orbit