  We study the effect of scalar leptoquark and $Z^\prime$ boson on the rare
decays of $D$ mesons involving flavour changing transitions $c \to u l^+ l^-
(l^\mp_i l^\pm_j)$. We constrain the new physics parameter space using the
branching ratio of the rare decay mode $D^0 \to \mu^+ \mu^-$ and the $D^0-\bar
D^0$ oscillation data. We compute the branching ratios, forward-backward
asymmetry parameters and flat terms in $D^{+(0)} \to \pi^{+(0)} \mu^+ \mu^-$
processes using the constrained parameters. The branching ratios of the lepton
flavour violating $D$ meson decays, such as $D^0 \to \mu e, ~\tau e$ and
$D^{+(0)} \to \pi^{+(0)} \mu^- e^+$ are also investigated.
