  Recent N-body simulations indicate that a thick disc of dark matter,
co-rotating with the stellar disc, forms in a galactic halo after a merger at a
redshift $z<2$. The existence of such a dark disc component in the Milky Way
could affect dramatically dark matter signals in direct and indirect detection.
In this letter, we discuss the possible signal enhancement in connection with
the characteristics of the local velocity distributions. We argue that the
enhancement is rather mild, but some subtle effects may arise. In particular,
the annual modulation observed by DAMA becomes less constrained by other direct
detection experiments.
