  Cadmium arsenide ($\rm Cd_3As_2$) is known for its inverted band structure
and ultra-high electron mobility. It has been theoretically predicted and also
confirmed by ARPES experiments to exhibit a 3D Dirac semimetal phase containing
degenerate Weyl nodes. From magneto-transport measurements in high quality
single crystals of $\rm Cd_3As_2$, a small effective mass $m^* \approx$ 0.05
$m_e$ is determined from the Shubnikov-de Haas (SdH) oscillations. In certain
field orientations, we find a splitting of the SdH oscillation frequency in the
FFT spectrum suggesting a possible lifting of the double degeneracy in accord
with the helical spin texture at outer and inner Fermi surfaces with opposite
chirality predicted by our \textit{ab initio} calculations. Strikingly, a large
antisymmetric magnetoresistance with respect to the applied magnetic fields is
uncovered over a wide temperature range in needle crystal of $\rm Cd_3As_2$
with its long axis along [112] crystal direction. It reveals a possible
contribution of intrinsic anomalous velocity term in the transport equation
resulting from a unique 3D Rashba-like spin splitted bands that can be obtained
from band calculations with the inclusion of Cd antisite defects.
