  The processes of $\eta_c (\eta_c')\to VV$ are supposed to be suppressed by
the helicity selection rule (HSR) but found to be rather important decay modes
in experiment for $\eta_c$. We try to distinguish the short-distance
transitions via the singly disconnected Okubo-Zweig-Iizuka (SOZI) processes and
the doubly disconnected (DOZI) processes in $\eta_c (\eta_c')\to VV$. It shows
that the SOZI processes can be related to the $\eta_c(\eta_c')$ wavefunctions
at the origin. Therefore, a relation of the decay branching ratio fraction
between these two decay channels can be established. Such a relation is similar
to that for $J/\psi$ and $\psi^\prime\to VP$, where the so-called "$\rho\pi$
puzzle" has been existed for a while. We also show that the intermediate
charmed meson loop transitions provide an evading mechanism for the DOZI
processes. This contribution would turn out to be more important in
$\eta_c^\prime\to VV$. As a consequence, it may produce significant deviations
from the SOZI-dominant scenario. Future experimental measurement of the
$\eta_c^\prime\to VV$ by BESIII should be able to clarify the DOZI-evading
mechanisms.
