  B. Totaro showed \cite{totaro} that the rational cohomology of configuration
spaces of smooth complex projective varieties is isomorphic as an algebra to
the $E_2$ term of the Leray spectral sequence corresponding to the open
embedding of the configuration space into the Cartesian power. In this note we
show that the isomorphism can be chosen to be compatible with the mixed Hodge
structures. In particular, we prove that the mixed Hodge structures on the
configuration spaces of smooth complex projective varieties are direct sums of
pure Hodge structures.
