You can always do it if the transfer function has non-repeated roots. For example, if you can put your transfer function into this form:
$$G(s) = \frac{Y(s)}{U(s)} = \frac{c_1}{s-p_1} + \dots + \frac{c_n}{s-p_n}$$
then, it is equivalent to:
$$\begin{align} \begin{bmatrix}\dot{x}_1 \\\ \dot{x}_2 \\\ \vdots \\\ \dot{x}_n\end{bmatrix} &= \begin{bmatrix}p_1 & 0 & \dots & 0 \\\ 0 & p_2 & \dots & 0 \\\ \vdots & \vdots & \ddots & \vdots \\\ 0 & 0 & \dots & p_n\end{bmatrix}\begin{bmatrix}x_1 \\\ x_2 \\\ \vdots \\\ x_n\end{bmatrix} + \begin{bmatrix}1 \\\ 1 \\\ \vdots \\\ 1\end{bmatrix}u \\\ y &= \begin{bmatrix}c_1 & c_2 & \dots & c_n\end{bmatrix}\begin{bmatrix}x_1 \\\ x_2 \\\ \vdots \\\ x_n\end{bmatrix} \end{align}$$