A relativistic quantum equation for free particles of any spin in a global curved spacetime is derived. Using this equation, it is demonstrated that in axially symmetric spacetimes, the wave function factorizes into a reduced wave function and an analytically determined normalization function. In spherical coordinates, the reduced wave function splits into a reduced angular wave function identically the same as in a flat Minkowski spacetime and a radial wave function which satisfies a second order non-homogeneous differential equation with nonhomogeneous terms depending on the ratio of time to space curvatures.
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