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For complex manifolds, the Riemann-Hilbert correspondence generalizes the classical correspondence between finite dimensional local systems and vector bundles with connections to perverse sheaves and regular holonomic D-modules. These later objects are in fact microlocal in nature that they can be regarded as living on the cotangent bundles, and the correspondence admits a microlocalization as well. Continuing from an earlier joint work with Côté, Nadler, and Shende, we will globalize this correspondence to general complex contact manifolds in an upcoming work.