Cd₃As₂ is a 3D Dirac semimetal with doubly degenerate band crossings at isolated points in the bulk Brillouin zone. It can also host gapless surface states. In Dirac and Weyl semimetals, a giant planar Hall effect (PHE) has been predicted to be associated with the chiral anomaly. In this talk, we will discuss our measurements of the PHE in (001) and (112) oriented epitaxial thin films of Cd₃As₂ having a wide range of film thicknesses. We show that the PHE depends sensitively on the Fermi level. Studies of films of different thickness allow us to distinguish the contributions of bulk and surface states. We will discuss the different mechanisms that give rise to the PHE in these films.