In the framework of the two-center shell model we calculate the nearest neighbor level spacing distribution and spectral rigidity of single-particle energy levels of heavy nuclei when the shape parameters are changed systematically. In the two cases of the single-particle Hamiltonian with and without the spin-orbit coupling l โข s and square angular momentum l 2 terms, the shape parameter regions are determined respectively, in which both of the spacing distribution and spectral rigidity approach the predictions of the Gaussian orthogonai ensemble of random matrix theory. In both cases it is shown that a considerable octupole-like deformation is necessary to induce the chaotic single-particle motion, Moreover, the occurrence of the chaotic motion not only appears in the heavy nuclei with oblate shapes but also in prolate ones with a proper neck. The neck appreciably influences the occurrence of the chaotic motion when the separation between the two centers is medium or larger. It is exhibited that the level repulsion which is strongly related to the nuclear deformation govems the regularity (chaoticity) of the single-particle motion. We find that the l-s term obviously favors the chaotic motion, however, the 12 term only slightly affects the chaotic motion. In addition, it is implied that when the two terms are taken into account, the chaotic motion occurs even in very elongated nuclei.