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In this paper, we attempt to implement the neutrino $\mu$-$\tau$ reflectionsymmetry (which predicts $\theta^{}_{23} = \pi/4$ and $\delta = \pm \pi/2$ aswell as trivial Majorana phases) in the minimal seesaw (which enables us to fixthe neutrino masses). For some direct (the preliminary experimental hintstowards $\theta^{}_{23} \neq \pi/4$ and $\delta \neq - \pi/2$) and indirect(inclusion of the renormalization group equation effect and implementation ofthe leptogenesis mechanism) reasons, we particularly study the breakings ofthis symmetry and their phenomenological consequences.

Neutrino mu-tau reflection symmetry and its breaking in the minimal seesaw