  Structural, magnetic, and dielectric properties of Sm$_2$CoMnO$_6$ have been
studied. X-ray diffraction and Rietveld analysis show that the sample
crystallizes in the monoclinic structure with \textit{P2$_1$/n} space group.
Magnetic study shows that the sample undergoes a paramagnetic to ferromagnetic
phase transition around $T_c$ $\sim$148 K and a low-temperature ordering of
Sm$^{3+}$ moments. Temperature-dependent Raman study shows spin-phonon coupling
present in this material. Dielectric response of Sm$_2$CoMnO$_6$ shows strong
frequency dependence with large dispersion and large dielectric constant.
Deviated from ideal Debye's model is found in impedance spectroscopy. Further,
the activation energy obtained from tangent loss and complex impedance suggests
that the relaxation process is due to electron hopping. AC conductivity has
been studied to understand the conduction mechanism. The detailed analysis of
AC conductivity shows that quantum mechanical tunneling of charges is involved
in the conduction mechanism. The exponent obtained from AC conductivity
measurements confirms the non-Debye's nature of Sm$_2$CoMnO$_6$.
