  Let $H$ be a connected $m$-uniform hypergraph, and let $\mathcal{A}(H)$ be
the adjacency tensor of $H$ whose spectrum is simply called the spectrum of
$H$. Let $s(H)$ denote the number of eigenvectors of $\mathcal{A}(H)$
associated with the spectral radius, and $c(H)$ denote the number of
eigenvalues of $\mathcal{A}(H)$ with modulus equal to the spectral radius,
which are respectively called the stabilizing index and cyclic index of $H$.
Let $\bar{H}$ be a $k$-fold covering of $H$ which can be obtained from some
permutation assignment in the symmetric group $\mathbf{S}_k$ on $H$. In this
paper, we first characterize the connectedness of $\bar{H}$ by its incidence
graph and the permutation assignment, and then investigate the relationship
between the spectral property of $H$ and that of $\bar{H}$. By applying module
theory and group representation, if $\bar{H}$ is connected, we prove that $s(H)
\mid s(\bar{H})$ and $c(H) \mid c(\bar{H})$. In particular, when $\bar{H}$ is a
$2$-fold covering of $H$, if $m$ is even, we show that regardless of
multiplicities, the spectrum of $\bar{H}$ contains the spectrum of $H$ and the
spectrum of a signed hypergraph with $H$ as underlying hypergraph; if $m$ is
odd, we give an explicit formula for $s(\bar{H})$. We also find some
differences on the spectral property between hypergraph coverings and graph
coverings by examples.
