  We analyze joint angular distributions of a charmonium decay to the
$\Xi\bar\Xi$ pair using the $\Xi\to\Lambda\pi\to p\pi^-\pi$ weak decay chain
for the cascade and the charge conjugated mode for the anticascade. The decays
allow a direct comparison of the baryon and antibaryon decay properties and a
sensitive test of CP symmetry in the strange baryon sector. We show that all
involved decay parameters can be determined separately in vector and
(pseudo)scalar charmonia decays into $\Xi\bar\Xi$ due to the spin correlations
between the weak decay chains. Contrary to the recently measured $e^+e^-\to
J/\psi\to \Lambda\bar\Lambda$ process, the transverse polarization of the
cascade is not needed and has almost no impact on the uncertainties of the
decay parameters.
