Hypothesis testing for the correlation coefficient (at least one of them) is based on a t-distribution of the test statistic $t=\frac{r}{\sqrt{(1-r^2)/(N-2)}}$ where $r$ is the sample correlation coefficient and $N$ is the number of cases. 

Can someone tell me what assumptions are made in order for this $t$ to have a $t$-distribution ? I assume that bivariate normality is one of them ?