The aim of this paper is two folded. Firstly, we study the validity of the
Pohozaev-type identity for the Schr\"{o}dinger operator $$A_\la:=-\D
-\frac{\la}{|x|^2}, \q \la\in \rr,$$ in the situation where the origin is
located on the boundary of a smooth domain $\Omega\subset \rr^N$, $N\geq 1$.
The problem we address is very much related to optimal Hardy-Poincar\'{e}
inequality with boundary singularities which has been investigated in the
recent past in various papers. In view of that, the proper functional framework
is described and explained.