The trace of tensors that account for chiroptical response of the H2O2 molecule is a function of the HO-OH dihedral angle. It vanishes at 0 degrees and 180 degrees, due to the presence of molecular symmetry planes, but also for values in the range 90-100 degrees of this angle, in which the molecule is unquestionably chiral. Such an atypical effect is caused by counterbalancing contributions of diagonal tensor components with nearly maximal magnitude but opposite sign, determined by electron flow in open or closed helical paths, and associated with induced electric and magnetic dipole moments and anapole moments. For values of dihedral angle external to the 90-100 interval, the helical paths become smaller in size, thus reducing the amount of cancellation among diagonal components. Shrinking of helical paths determines the appearance of extremum values of tensor traces approximately at 50 degrees and 140 degrees dihedral angles.