  Measurements on the weak decay asymmetry parameters of charmed baryon, say
$\Xi_c$, provide more information on the $W$-emission and $W$-exchange
mechanisms controlled by the strong and weak interactions. Taking advantage of
the spin polarization in the charmed baryon decays, we investigate the
possibility to measure the weak decay asymmetry parameters in the
$e^{+}e^{-}\to \Xi_c^0\bar\Xi_c^0$ process. We analyze the transverse
polarization spontaneously produced in this process and spin transfer in the
subsequent $\Xi_c$ decays. The sensitivity to measure the asymmetry parameters
are estimated for the decay $\Xi_c\to\Xi \pi$.
