  We present a study of correlations between D and $\bar{D}$ mesons produced in
500 GeV/$c$ $\pi^-$-nucleon interactions, based on data from experiment E791 at
Fermilab. We have fully reconstructed $791 \pm 44$ charm meson pairs to study
correlations between the transverse and longitudinal momenta of the two D
mesons and the relative production rates for different types of D meson pairs.
We see slight correlations between the longitudinal momenta of the D and the
$\bar D$, and significant correlations between the azimuthal angle of the D and
the $\bar D$. The experimental distributions are compared to a
next-to-leading-order QCD calculation and to predictions of the {\sc
Pythia/Jetset} Monte Carlo event generator. We observe less correlation between
transverse momenta and different correlations between longitudinal momenta than
these models predict for the default values of the model parameters. Better
agreement between data and theory might be achieved by tuning the model
parameters or by adding higher order perturbative terms, thus contributing to a
better understanding of charm production.
  The relative production rates for the four sets of charm pairs,
$D^0\bar{D}^{0}$, $D^0D^-$, $D^+\bar{D}^{0}$, $D^+D^-$, as calculated in the
{\sc Pythia/Jetset} event generator with the default parameters, agree with
data as far as the relative ordering, but predict too many $D^+\bar{D}^{0}$
pairs and too few $D^+D^-$ pairs.
