The modular symbols are defined as $\langle \gamma, f\rangle=-2\pi i \int_{a}^{\gamma a }f(\tau )\d\tau,$ where $f(\tau )$ is a holomorphic cusp form of weight $2$ for $\Gamma$ and $\gamma\in \Gamma$. We prove that on a surface with cusps the modular symbols appropriately normalized and ordered according to $c^2+d^2$, where $(c, d)$ is the second row of $\gamma$ have a binormal

distribution in the complex plane with correlation coefficient $0$. We examine various possible generalisations.