Given an independent and identically distributed sample of angles from some absolutely continuous circular random variable with unknown probability density function \( f \), in this work we study the problem of testing the hypothesis on whether f is the uniform distribution on the circle. For this purpose we consider a Bickel-Rosenblatt type test statistic (\( L^2 \) distance) based on the Parzen-Rosenblatt type estimator for circular data. The asymptotic behaviour of the proposed test procedure for fixed and non-fixed bandwidths is studied. From a finite sample point of view the power performance of the tests associated with different bandwidths depends on the considered bandwidth which acts as a tuning parameter. The automatic selection of this tuning parameter, the choice of which is crucial to obtaining a performing test procedure, is also addressed in this work, and comparisons are made with other existing uniformity tests through a simulation study.