Reference for showing that $\mathcal{O}(G) \cong U(\mathfrak{g})^{\circ}$ when $G$ is connected and simply connected

Let $$G$$ be an algebraic group. We can try to reconstruct $$G$$ from its lie algebra $$\mathfrak{g}$$, but the best we get in general is a formal group scheme $$\operatorname{Spf}(U(\mathfrak{g})^*)$$, where $$U(\mathfrak{g})$$ is the universal enveloping algebra of $$\mathfrak{g}$$.

However, I have heard that certain conditions provide for a full reconstruction of $$G$$. Namely, if $$G$$ is connected and simply connected, then there is an isomorphism $$\mathcal{O}(G) \rightarrow U(\mathfrak{g})^{\circ}$$, where $$U(\mathfrak{g})^{\circ}$$ is the Hopf dual of $$U(\mathfrak{g})$$.

I can’t seem to find a reference for this. Could someone please provide one?