We consider a linear mixed-effects model where $Y_{k,j}= \alpha_k + \beta_k t_{j} +\varepsilon_{k,j}$ is the observed value for individual $k$ at time $t_j$, $k=1,\ldots, N$, $j=1,\dots, J$. The random effects $\alpha_k$, $\beta_k$ are independent identically distributed random variables with unknown densities $f_\alpha$ and $f_\beta$ and are independent of the noise. We develop nonparametric estimators of these two densities, which involve a cutoff parameter. We study their mean integrated square risk and propose cutoff-selection strategies, depending on the noise distribution assumptions. Lastly, in the particular case of fixed interval between times $t_j$, we show that a completely data driven strategy can be implemented without any knowledge on the noise density. Intensive simulation experiments illustrate the method.