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A class of critical Kirchhoff-Poisson systems on Heisenberg group was studied. Due to the existence of critical and non-local terms, the space embedding was not compact. Under the assumptions that the nonlinear terms were appropriate, the space compactness was overcame by the variational method and established the existence of at least one solution to this system. Furthermore, using deformation lemma and topological degree theory, it was proved that the solution was a sign-changing solution. [ABSTRACT FROM AUTHOR]