Dipole moments of (2)Sigma and (2)Pi states of CN radical at different internuclear distances are reported using the multireference coupled cluster (MRCC) linear response approach. We also report as a by product the potential energy surface, equilibrium geometry and harmonic frequency of CN radical states that agree well with those calculated using multi-configuration quasi-degenerate perturbation theory (MCQDPT). The dipole moment of the ground state of the radical is in excellent agreement with the experimental value. Dipole moments are also calculated using MRCI using bigger complete active space and state specific orbitals and results of both methods agree well.