Constraints on proximity-induced ferromagnetism in a Dirac semimetal <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>Cd</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mi>As</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>)</mml:mo><mml:mo>/</

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$^3$).