The universal statistics of energy levels that emerge in disordered electronic systems near the Anderson-transition point is studied. It is shown that the two-level correlation function (TLCF) has a power law tail that is characterized by a non-trivial exponent γ < 1. The scaling relationship between γ and the correlation length exponentv is derived. A statistical hypothesis involving two kinds of energy levels is proposed to explain the sum rule violation for the critical TLCF.