  Frequency-dependent and temperature-dependent dielectric measurements are
performed on double perovskite Tb$_2$NiMnO$_6$. The real ($\epsilon_1$) and
imaginary ($\epsilon_2$) parts of dielectric permittivity show three plateaus
suggesting dielectric relaxation originating from bulk, grain boundaries and
the sample-electrode interfaces respectively. The temperature and frequency
variation of $\epsilon_1$ and $\epsilon_2$ are successfully simulated by a $RC$
circuit model. The complex plane of impedance, $Z'$-$Z"$, is simulated using a
series network with a resistor $R$ and a constant phase element. Through the
analysis of frequency-dependent dielectric constant using modified-Debye model,
different relaxation regimes are identified. Temperature dependence of dc
conductivity also presents a clear change in slope at, $T^*$. Interestingly,
$T^*$ compares with the temperature at which an anomaly occurs in the phonon
modes and the Griffiths temperature for this compound. The components $R$ and
$C$ corresponding to the bulk and the parameter $\alpha$ from modified-Debye
fit tend support to this hypothesis. Though these results cannot be interpreted
as magnetoelectric coupling, the relationship between lattice and magnetism is
marked.
