A bilayer quantum Hall (QH) state is a fascinating system which is constructed by adding the layer degree of freedom, which is represented as "pseudospin", to an ordinary monolayer QH system. As a result of the combination of both spins and pseudospins, the ν = 2 bilayer QH state has revealed a variety of quantum phases. Recently the magnetoresistance peak was found in the ν = 1 bilayer QH state around the commensurate-incommensurate (C-IC) transition point. In this work we have carried out similar quantum magnetotranport experiments in the ν = 2 bilayer QH state while tilting a sample in a magnetic field. Although no anomalous behavior in magnetoresistance was found below the tilting angle of θC = 61°, a peak has been observed above θC. This structure resembles the peak reported in the ν = 1 QH state, and we expect it to be a signal of a phase transition in the ν = 2 QH state. We analyze this anomaly whether it results from the level crossing or the C-IC transition.