This study presents a new method for measuring similarity between two Gaussian mixture models (GMMs) to discover how to compensate for variations in the topology of adaptive hidden Markov models (HMM). The aims of the proposed scheme is to determine whether a new state topology with different variations should be added to existing acoustic models in response to the addition of training data. The testing of two Gaussian densities is frequently used in the sharing of parameters between Gaussian components of HMM. In this work, we extend such hypothesis to measure similarities between two GMMs and estimate the statistic from the proposed test through the summation of two gamma distributions. A new HMM topology is automatically generated according to a level of significance. The dataset-dependent characteristics and variations are handled with an adaptive HMM topology. Experiments on speech recognition tasks show that the proposed testing scheme performs significantly better than the standard HMM with a comparable size of parameters.