  Breaking time-reversal symmetry in a Dirac semimetal Cd$_3$As$_2$ through
doping with magnetic ions or by the magnetic proximity effect is expected to
cause a transition to other topological phases (such as a Weyl semimetal). To
this end, we investigate the possibility of proximity-induced ferromagnetic
ordering in epitaxial Dirac semimetal (Cd$_3$As$_2$)/ferromagnetic
semiconductor (Ga$_{1-x}$Mn$_x$Sb) heterostructures grown by molecular beam
epitaxy. We report the comprehensive characterization of these heterostructures
using structural probes (atomic force microscopy, x-ray diffraction, scanning
transmission electron microscopy), angle-resolved photoemission spectroscopy,
electrical magneto-transport, magnetometry, and polarized neutron
reflectometry. Measurements of the magnetoresistance and Hall effect in the
temperature range 2 K - 20 K show signatures that could be consistent with
either a proximity effect or spin-dependent scattering of charge carriers in
the Cd$_3$As$_2$ channel. Polarized neutron reflectometry sets constraints on
the interpretation of the magnetotransport studies by showing that (at least
for temperatures above 6 K) any induced magnetization in the Cd$_3$As$_2$
itself must be relatively small ($<$ 14 emu/cm$^3$).
