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\begin{abstract}
Let $B_{n,k}$ and $A_{n}=\sum_{j=1}^{n}B_{n,j}$ with $A_0=1$ be,
respectively, the $(n,k)^{\rm th}$ partial and the $n^{\rm th}$ complete
Bell polynomials with indeterminate arguments $x_1,x_2,\ldots$. 
Congruences for $A_{n}$ and $B_{n,k}$ with respect to a prime number have
been studied by several authors. In the present paper, we propose
some results involving congruences for $B_{n,k}$ when the arguments
are integers. We give a relation between Bell polynomials and we apply it
to several congruences. The obtained congruences are
connected to binomial coefficients.
\end{abstract}

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