Let $f : X \to \operatorname{Spec}(R)$ be a flat and projective morphism of schemes over $\mathbb{C}$, where $R$ is a DVR. Assume additionally that the fibers of $f$ are Gorenstein and seminormal (in particular reduced). Let $i : X_0 \to X$ denote the closed immersion of the special fiber.
Is it then the case that the morphism of tangent sheaves $i^*\mathcal{T}_{X / R} \to \mathcal{T}_{X_0 / \mathbb{C}}$ is an isomorphism?