  The neutrino $\mu$-$\tau$ reflection symmetry has been attracting a lot of
attention as it predicts the interesting results $\theta^{}_{23} = \pi/4$ and
$\delta = \pm \pi/2$. But it is reasonable to consider breakings of such a
symmetry either from the theoretical considerations or on the basis of
experimental results. We thus perform a systematic study for the possible
symmetry-breaking patterns and their implications for the mixing parameters.
The general treatment is applied to some specific symmetry breaking arising
from the renormalization group effects for illustration.
