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We present firstly the equation of motion for the test scalar particlecoupling to the Chern-Simons invariant in Kerr black hole spacetime by theshort-wave approximation. We have analyzed the dynamical behaviors of the testcoupled particles by applying techniques including Poincar\'e sections, fastLyapunov exponent indicator, bifurcation diagram and basins of attraction. Itis shown that there exists chaotic phenomenon in the motion of scalar particleinteracted with the Chern-Simons invariant in a Kerr black hole spacetime. Withthe increase of the coupling strength, the motion of the coupled particles forthe chosen parameters first undergoes a series of transitions betweens chaoticmotion and regular motion and then falls into horizon or escapes to spatialinfinity. Thus, the coupling between scalar particle and Chern-Simons invariantyields the richer dynamical behavior of scalar particle in a Kerr black holespacetime.

Chaotic motion of scalar particle coupling to Chern-Simons invariant in Kerr black hole spacetime