  We investigate the parity ($\mathcal{P}$) and time-reversal ($\mathcal{T}$)
symmetry violating effects in the CdH molecule and perform the relativistic
coupled-cluster calculation of the molecular parameters- $E_\text{eff}$,
$W_\text{s}$ and $W_\text{M}$ related to the electric dipole moment of electron
(eEDM) interaction, the scalar-pseudoscalar (S-PS) nucleus-electron neutral
current coupling and the nuclear magnetic quadrupole moment (MQM) interaction
with electrons, respectively. We also compute the molecular dipole moment and
the magnetic hyperfine structure coupling constant of CdH. The value of
$E_\text{eff}$, $W_\text{s}$ and $W_\text{M}$ obtained by us in the said
molecule are 12.2 GV/cm, 14.0 kHz and $0.82\times$10$^{33}$ Hz/e cm$^2$,
respectively, within an uncertainty of 10\%. Furthermore, we study the trend of
electron-correlation in the computed properties of CdH and that of the
$\mathcal{P,T}$-odd parameters in the group-12 monohydrides (i.e., ZnH, CdH,
and HgH).
