  Let $T>0,\alpha>\frac12$. In the present paper we consider the
$\alpha$-Brownian bridge defined as $dX_t=-\alpha\frac{X_t}{T-t}dt+dW_t,~ 0\leq
t< T$, where $W$ is a standard Brownian motion. We investigate the optimal rate
of convergence to normality of the maximum likelihood estimator (MLE) for the
parameter $ \alpha $ based on the continuous observation $\{X_s,0\leq s\leq
t\}$ as $t\uparrow T$. We prove that an optimal rate of Kolmogorov distance for
central limit theorem on the MLE is given by $\frac{1}{\sqrt{|\log(T-t)|}}$, as
$t\uparrow T$. First we compute an upper bound and then find a lower bound with
the same speed using Corollary 1 and Corollary 2 of \cite{kp-JVA},
respectively.
