  Given a sample of a random variable supported by a smooth compact manifold
$M\subset \mathbb{R}^d$, we propose a test to decide whether the boundary of
$M$ is empty or not with no preliminary support estimation. The test statistic
is based on the maximal distance between a sample point and the average of its
$k_n$-nearest neighbors. We prove that the level of the test can be estimated,
that, with probability one, its power is one for $n$ large enough, and that
there exists a consistent decision rule. Heuristics for choosing a convenient
value for the $k_n$ parameter and identifying observations close to the
boundary are also given. We provide a simulation study of the test.
