  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 paper,
first we study the Laplacian spectrum of $\Gamma'(\mathbb{Z}_n)$. We show that
the graph $\Gamma'(\mathbb{Z}_{pq})$ is Laplacian integral. Further, we obtain
the Laplacian spectrum of $\Gamma'(\mathbb{Z}_n)$ for $n = p^{n_1}q^{n_2}$,
where $n_1, n_2 \in \mathbb{N}$ and $p, q$ are distinct primes. In order to
study the Laplacian spectral radius and algebraic connectivity of
$\Gamma'(\mathbb{Z}_n)$, we characterized the values of $n$ for which the
Laplacian spectral radius is equal to the order of $\Gamma'(\mathbb{Z}_n)$.
Moreover, the values of $n$ for which the algebraic connectivity and vertex
connectivity of $\Gamma'(\mathbb{Z}_n)$ coincide are also described. At the
final part of this paper, we obtain the Wiener index of $\Gamma'(\mathbb{Z}_n)$
for arbitrary $n$.
