By employing the Riccati transformation technique some new oscillation criteria for the second-order neutral delay dynamic equation $$(y(t)+r(t)y({ au}(t)))^{{Delta}{Delta}}+p(t)y(delta(t))=0$$, on a time scale $mathbb{T}$ are established. Our results as a special case when $mathbb{T}=mathbb{R}$ and $mathbb{T}=mathbb{N}$ improve some well known oscillation criteria for second order neutral delay differential and difference equations, and when $mathbb{T}=q^{mathbb{N}}$, i.e., for second-order $q$-neutral difference equations our results are essentially new and can be applied on different types of time scales. Some examples are considered to illustrate the main results.