We present the results of analysis of the switching current during polarization reversal in wide field range in KTA single crystals. According to previously revealed stages of domain structure evolution, the switching current data have been separated into three parts. The first original hatching stage representing growth of streamer clusters with smooth current has been revealed. Fitting of the switching current by Kolmogorov-Avrami formula has allowed extracting the main characteristic times, which followed the activation field dependence. It has been demonstrated that the fraction of the area switched by hatching is almost the same for the whole field range.