Anxiety and depression are common comorbidities in chronic obstructive pulmonary disease (COPD) patients but are often under-diagnosed. We aimed to assess the suitability of the COPD Assessment Test (CAT) in screening anxiety and depression in patients with COPD. Stable COPD patients from a cross-sectional observational study were assessed by CAT. Anxiety and depression were identified using the Generalized Anxiety Disorder questionnaire (GAD-7) and Patient Health Questionnaire (PHQ-9), respectively. Logistic regression analysis and receiver operating characteristic curve analysis were used to identify factors associated with anxiety or depression and to calculate the predictive values. A total of 530 stable COPD patients were enrolled and of those, the proportions of anxiety and depression were 17.0% and 21.5%, respectively. The adjusted odds ratios of the CAT for the presence of anxiety and depression were 1.094 (95%CI: 1.057–1.131) and 1.143 (95%CI: 1.104–1.183), respectively. The CAT score had a significant predictive value for the presence of anxiety (AUC = 0.709) and depression (AUC = 0.791) with an optimum cutoff score of 15. However, the psychometric properties of CAT were undesirable, presenting high negative predictive value (NPV) but low positive predictive value (PPV). Among CAT items, analysis further showed that non-respiratory CAT components were superior to respiratory components in identifying both anxiety and depression. Our results indicated that CAT is more useful to exclude anxiety and depression rather than detect them.