  Roles of electron correlation effects in the determination of attachment
energies, magnetic dipole hyperfine structure constants and electric dipole
(E1) matrix elements of the low-lying states in the singly charged cadmium ion
(Cd$^+$) have been analyzed. We employ the singles and doubles approximated
relativistic coupled-cluster (RCC) method to calculate these properties.
Intermediate results from the Dirac-Hartree-Fock approximation, second-order
many-body perturbation theory and considering only the linear terms of the RCC
method are given to demonstrate propagation of electron correlation effects in
this ion. Contributions from important RCC terms are also given to highlight
importance of various correlation effects in the evaluation of these
properties. At the end, we also determine E1 polarizabilities ($\alpha^{E1}$)
of the ground and $5p \ ^2P_{1/2;3/2}$ states of Cd$^+$ in the {\it ab initio}
approach. We estimate them again by replacing some of the E1 matrix elements
and energies from the measurements to reduce their uncertainties so that they
can be used in the high precision experiments of this ion.
