  We investigate the recently suggested scheme of independent mass matrices for
neutrinos and antineutrinos. Such a CPT violating scheme is able to account for
all neutrino data with the three known flavors. For atmospheric neutrinos this
means that it is possible to have different mass squared differences driving
the oscillation for neutrinos and antineutrinos. We analyze the atmospheric and
K2K data within the simplest scheme of two neutrino oscillation, neglecting
electron neutrino oscillation. We find that the preferred region is close to
the CPT conserving mass spectra. However the spectra with the antineutrino mass
squared difference about or larger than 0.1 eV^2 and the neutrino mass squared
difference about 2 \times 10^{-3} eV^2 is not significantly disfavored. In this
parameter region the atmospheric data are independent of the antineutrino mass
squared difference. Therefore no useful constraint can be put on CPT violation
effects contributing to different masses for the neutrinos and antineutrinos.
