In highly rarefied gas flows, there appear nonequilibrium phenomena not only between translational and rotational energy modes (non-equipartition) but also deviation of rotational energy distribution from the Boltzmann distribution. To analyze these highly rarefied gas flows, we established the experimental system for 2R+2 N2-REMPI and applied it to the measurement of rotational temperature in a supersonic free molecular flow of nitrogen. In this study, a strong nonequilibrium in rotational energy mode has been found in a nitrogen free molecular flow. The data in the Boltzmann plot, obtained from the measured REMPI spectra, cannot be fitted by one line but approximately by two lines, revealing the non-Boltzmann distribution of rotational energy in the ground state. The mechanism of the deviation from the Boltzmann distribution is also discussed using the state-to-state transition rates for collisional relaxation.