  The contribution of ground state correlations (GSC) to the non--mesonic weak
decay of $^{12}_\Lambda$C and other medium to heavy hypernuclei is studied
within a nuclear matter formalism implemented in a local density approximation.
We adopt a weak transition potential including the exchange of the complete
octets of pseudoscalar and vector mesons as well as a residual strong
interaction modeled on the Bonn potential. Leading GSC contributions, at first
order in the residual strong interaction, are introduced on the same footing
for all isospin channels of one-- and two--nucleon induced decays. Together
with fermion antisymmetrization, GSC turn out to be important for an accurate
determination of the decay widths. Besides opening the two--nucleon stimulated
decay channels, for $^{12}_\Lambda$C GSC are responsible for 14% of the rate
$\Gamma_1$ while increasing the $\Gamma_{n}/\Gamma_{p}$ ratio by 4%. Our final
results for $^{12}_\Lambda$C are: $\Gamma_{\rm NM}=0.98$,
$\Gamma_{n}/\Gamma_{p}=0.34$ and $\Gamma_2/\Gamma_{\rm NM}=0.26$. The
saturation property of $\Gamma_{\rm NM}$ with increasing hypernuclear mass
number is clearly observed. The agreement with data of our predictions for
$\Gamma_{\rm NM}$, $\Gamma_n/\Gamma_p$ and $\Gamma_2$ is rather good.
