  We study the conditions under which the tangent bundle $(TM,G)$ of an
$n$-dimensional Riemannian manifold $(M,g)$ is conformally flat, where $G$ is a
general natural lifted metric of $g$. We prove that the base manifold must have
constant sectional curvature and we find some expressions for the natural
lifted metric $G$, such that the tangent bundle $(TM,G)$ become conformally
flat.
