$ \newcommand{\C}{{\Bbb C}} $Let $G$ be a connected semisimple algebraic group over the field of complex numbers $\C$. Assume that $G$ is simply connected: any surjective homomorphism with finite kernel $$G'\to G$$ where $G'$ is a connected semisimple algebraic group over $\C$, is an isomorphism.
From this we can deduce that the corresponding complex Lie group $G(\C)$ is simply connected in topological sense: any continuous loop $$ \theta\colon [0,1] \to G(\C)\qquad \text{such that}\quad \theta(0)=\theta(1)= 1_G$$ is contractible.
I am looking for a reference for this deduction.