In this note, we study the KoszulBrylinski homology of holomorphic Poisson manifolds. We show that it is isomorphic to the cohomology of a certain smooth complex Lie algebroid with values in the Evens-Lu-Weinstein duality module. As a consequence, we prove that the Evens-Lu-Weinstein pairing on KoszulBrylinski homology is nondegenerate. Finally, we compute the oszul-Brylinski homology for Poisson structures on ℂℙ1 × ℂℙ1.
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