In this paper, we consider a uniform circular array (UCA) of antennas at the base station (BS) and the mobile station (MS) and derive an exact closed-form expression for the spatial correlation present in the 3D multiple-input multiple-output (MIMO) channel constituted by these arrays. The underlying method leverages the mathematical convenience of the spherical harmonic expansion (SHE) of plane waves and the trigonometric expansion of Legendre polynomials. In contrast to the existing results, this generalized closed-form expression is independent of the form of the underlying angular distributions and antenna patterns. Verification is achieved with the help of simulation results, which highlight the dependence of spatial correlation on channel and array parameters. An interesting interplay between the mean angle of departure (AoD), angular spread and the positioning of the antennas in the array is demonstrated.