The electron distribution function is statistically examined from measurements by Thomson scattering at +or-7 cm off-axis points (about half of the minor radius, 13.5 cm) from the center of the vacuum vessel of the TPE-1RM15 reversed field pinch (RFP) machine. Four different RFP discharge conditions are examined at both ports on a shot-by-shot basis. The wavelength shift of the distribution function and corresponding poloidal current density are deduced so that the same bulk electron temperatures at both the inside (-7 cm) and outside (+7 cm) ports are obtained. The deviation of the distribution function from the shifted Maxwellian is examined from the difference in fitted temperature with different weighting functions. The results indicate that in two of the experimental groups, the plasma current density carried by the tail electrons above 2.6 keV exceeds that carried by the shifted bulk Maxwellian distribution. For all of the data groups, the ratio of the current density carried by tail electrons to the total current density has a positive correlation with both E/EC (=0.14-0.22) and eta k/ eta S, where EC is the critical electric field for thermal electrons to run away, and eta k and eta S, are the plasma resistivity estimated from the helicity balance equation and Spitzer's formula, respectively. These tail electrons observed in the core plasma of an RFP can be attributed to the origin of the high-energy electrons recently observed at the edge region of RFPs.