  We investigate the three-body decays of $\Lambda_c^*(2595)$ and
$\Lambda_c^*(2625)$ into $\Lambda_c \pi \pi$ by including a direct process
going through the two-pion coupling of $\Lambda_c^*\Lambda_c \pi \pi$ in
addition to the sequential processes going through $\Sigma_c(2455)$ and
$\Sigma_c^*(2520)$. The strength of the direct coupling is related to that of
the Yukawa coupling by the chiral partner structure between $\Lambda_c$'s and
$\Sigma_c$'s, while the strength of the Yukawa coupling is estimated by the
quark model. It is found that the direct process gives a considerable
contribution especially in the decay of $\Lambda_c^*(2625)$. A clear indication
of the direct process is seen in an asymmetric pattern in the angular
correlation between the two pions. We discuss the usefulness of the detailed
analysis of the decays for the study of the structure of $\Lambda_c^*$.
