  The LHCb bounds on the branching ratio of rare decay $D^0 \to \mu^+ \mu^-$
and the constraints on the branching ratio of $D^+ \to \pi^+ \mu^+ \mu^-$ in
the nonresonant regions enable us to improve constraints on new physics
contributions. Using the effective Lagrangian approach we determine sizes of
the Wilson coefficients allowed by the existing LHCb bounds on rare charm
decays. Then we discuss contributions to rare charm meson decay observables in
several models of new physics: a model with an additional spin-1 weak triplet,
leptoquark models, Two Higgs doublets model of type III, and a $Z'$ model. Here
we complement the discussion by $D^0 - \bar D^0$ oscillations data. Among
considered models, only leptoquarks can significantly modify Wilson
coefficients. Assuming that the differential decay width for $D^+ \to \pi^+
\mu^+ \mu^-$ receives NP contribution, while the differential decay width for
$D^+ \to \pi^+ e^+ e^-$ is Standard Model-like, we find that lepton flavor
universality can be violated and might be observed at high dilepton invariant
mass.
