Let $C_*$ and $D_*$ be chain complexes of vector spaces over a field $k$. The classical Kunneth theorem states that the homology of the complex $Tot(C_* \otimes D_*)$ is isomorphic to $H_*(C) \otimes H_*(D)$.
I am interested in a similar statement for the hom functor. Namely, it is also true that $H^*(\hom(C_*,D_*)) \cong \hom(H_*(C), H_*(D))$
If so, is there a reference for this fact?