  Let $R$ be a ring with unity. The cozero-divisor graph of a ring $R$, denoted
by $\Gamma'(R)$, is an undirected simple graph whose vertices are the set of
all non-zero and non-unit elements of $R$, and two distinct vertices $x$ and
$y$ are adjacent if and only if $x \notin Ry$ and $y \notin Rx$. In this
article, we extend some of the results of [24] to an arbitrary ring. In this
connection, we derive a closed-form formula of the Wiener index of the
cozero-divisor graph of a finite commutative ring $R$. As applications, we
compute the Wiener index of $\Gamma'(R)$, when either $R$ is the product of
ring of integers modulo $n$ or a reduced ring. At the final part of this paper,
we provide a SageMath code to compute the Wiener index of the cozero-divisor
graph of these class of rings including the ring $\mathbb{Z}_{n}$ of integers
modulo $n$.
