Several methods have been developed for screening mentally impaired patients using biomarkers, but these methods are invasive and costly. Self-administered tests are also used as screening methods. They are non-invasive and relatively simple, but they cannot eliminate the influence of reporting bias. On the other hand, the authors have conducted studies on technologies for inferring the mental state of persons from their voices. Analysis using voice has the advantage of being noninvasive and easy to perform. This study proposes a vocal index that will distinguish between a healthy person and a bipolar I or II patient using a polytomous logistic regression analysis with patients with bipolar disorder as subjects. When the subjects were classified using the prediction model obtained from the analysis, the subjects were categorized into three groups with an accuracy of approximately 67%. This result suggested that the vocal index could be a new evaluation index for discriminating between subjects with and those without bipolar disorder.