  We consider scalar field perturbations in the background of black holes
immersed in perfect fluid dark matter (PFDM). We find, by using the sixth order
Wentzel-Kramers-Brillouin (WKB) approximation, that the longest-lived modes are
the ones with higher angular number, for a scalar field mass smaller than a
critical value, known as anomalous decay rate of the quasinormal modes, while
that beyond this critical value the behaviour is inverted. Moreover, we show
that it is possible to recover the real part of the quasinormal frequencies
(QNFs), the imaginary part of the QNFs, and the critical scalar field mass, of
the Schwarzschild background for different values of the PFDM intensity
parameter $k$, respectively. For values of $k$ smaller than these values, the
mentioned quantities are greater than the Schwarzschild background. However,
beyond of these values of $k$, these quantities are smaller than the
Schwarzschild background.
