  With the primary motivation of probing the quark substructure of scalar
mesons, a generalized linear sigma model for the lowest and the next-to-lowest
scalar and pseudoscalar mesons is employed to investigate several semi-leptonic
decays of $D$ mesons. The free parameters of the model (in its leading
approximation) have been previously determined from fits to mass spectra and
various low-energy parameters. With these fixed parameters, the model has
already given encouraging predictions for different low-energy decays and
scattering, as well as for semileptonic decay channels of $D_s^+$ that include
a scalar meson in the final state. In the present work, we apply the same model
(in its leading order with the same fixed parameters) to different
semi-leptonic decay channels of $D_s^+$, $D^+$ and $D^0$ and thereby further
test the model and its predictions for the quark substructure of scalar mesons.
We find that these predictions are in reasonable agreement with experiment.
