  The scintillation decay time constant of a ZnWO$_4$ crystal irradiated with
$\alpha$-particles from $^{241}$Am was precisely investigated, and was found to
depend on the incident direction of the $\alpha$-particles on the crystal. The
longest decay time constant ($24.3\pm0.6~\mu$s) was obtained on the surface
perpendicular to the b-axis of the crystal (Surface B). On Surfaces A and C,
the decay constants were $20.0$ and $21.3\pm0.2~\mu$s, respectively. The
scintillation yield of the ZnWO$_4$ was also anisotropic and depended on the
incident direction of the heavy particles. The maximum yield was achieved on
surface B, suggesting a correlation between the light yield and scintillation
decay time constant of ZnWO$_4$ crystals.
