  The most sensitive experimental searches for $D-\bar D$ mixing use $D^0 \to
K^+ \pi^-$ decays. It is often assumed that effects of New Physics and, in
particular, CP violation, can appear through the mixing, while the $c \to d u
\bar s$ decay amplitude cannot have significant contributions from New Physics
and is, therefore, CP conserving to a good approximation. We examine this
assumption in two ways. First, we calculate the contributions to the decay in
various relevant models of New Physics: Supersymmetry without R-parity,
multi-scalar models, left-right symmetric models, and models with extra quarks.
We find that phenomenological constraints imply that the New Physics
contributions are indeed small compared to the standard model doubly Cabibbo
suppressed amplitude. Second, we show that many of our constraints hold
model-independently. We find, however, one case where the model-independent
bound is rather weak and a CP violating contribution of order 30% is not
excluded.
