The objective of this study is to investigate the nature of the magnetic field relaxation process associated with tail current disruption on the basis of magnetic field measurements collected in the near-Earth tail regions. In detail, using magnetic field data for three current disruption (CD) events as observed by AMPTEE/CCE spacecraft, we investigate the scaling features of the probability distribution functions (PDFs) of the magnetic field fluctuations at different timescales τ. The PDFs of magnetic field fluctuations in non-MHD domain (i.e., below the proton gyroperiod) show non-Gaussian tails and the probability of return Pτ(0) scales in this domain as τ-α with α > 1/2, which is compatible with a L¿vy statistics. Conversely, the scaling of the PDFs of the CD magnetic fluctuations in the magnetohydrodynamic (MHD) regime is compatible with a classical Brownian motion α ~ 1/2. These findings are discussed in terms of an anomalous diffusion process, involving the magnetic field relaxation during CD. Furthermore, the relevance of these results of a non-Gaussian statistics at the shorter timescales is discussed in connection with the non-MHD nature of the CD phenomenon.