The neutrino $μ$-$τ$ reflection symmetry has been attracting a lot of attention as it predicts the interesting results $\theta^{}_{23} = π/4$ and $δ = ± π/2$. But it is reasonable to consider breaking of this 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. And the general treatment will be applied to some specific symmetry breaking arising from the renormalization group running effect for illustration. ; Comment: 16 pages, 5 figures, 5 tables