Let $\rho:E\to M$ be a smooth fibre bundle with fibre $F$, and let $s:M\to E$ be a section satisfying $\rho\circ s=\operatorname{id}_M$. Let $I$ be an index set, and let $(\Phi_i:\rho^{-1}(U_i)\to U_i\times F)_{i\in I}$ be a smooth bundle atlas. Then $s$ is smooth iff for every $i\in I$, the associated representative $(s|_{U_i})_{\Phi_i}:U_i\to F$ is smooth.