A lot of actions have recently been taken to support Government 2.0 movement. As the number of the actions increase, many people submit greater number of complaint reports by phone or mobile devices, and make sure the situation reported with each other. According to the actions, the delay in taking action of the government side becomes more clearly identified due to overloads of the government side to deal with the activities. To remedy the above situations, it increases of importance to develop an efficient approach to deal with the complaint reports. Automatic classification of the complaint reports, or estimation and extraction of demanding sentences from the reports are contributory to the approach. In this paper, we propose a method of automatically estimating categories of the complaint reports as a first step. We conducted experiments of estimating categories of the complaint reports. The experiment results showed the following findings: (1) Feature selection is a key to improve the F-score of estimating categories of complaint reports. The percentage of the words strongly effective for the category estimation is about 3.9% of the entire distinct words. (2) Proposed Mutual-Information-based methods outperform the F-score of a conventional Random-Forest-based method. (3) The F-score performance of estimating a category depends on the ambiguity level of the category. In particular, the F-score of estimating categories of a complaint report assigned multiple categories is 1.5 times worse than that of a complaint report assigned single category.