Introduction The Cognitive Function Score (CFS) is a public scale for assessing the activities of daily living (ADL) in older adults with dementia in Japan. In contrast, the scores of the revised Hasegawa's dementia scale (HDS-R), an easy-to-use dementia screening tool developed in Japan, are significantly correlated with mini-mental state examination scores and are widely utilized in various countries. This novel study aimed to elucidate the previously unexplored criterion-related validity of the CFS and HDS-R and the Bedriddenness Rank (BR), Barthel Index (BI), and Katz Index (KI). Methods This was a multicenter retrospective study and a secondary analysis of our previous study. The study included patients aged ≥ 20 years hospitalized in chronic care settings between April 1, 2018, and March 31, 2021. We collected data from medical charts on admission, including age, sex, the BR, CFS, BI, KI, and HDS-R scores. Correlations between the CFS and HDS-R score, as well as between the BR and BI or KI, were analyzed using Spearman's rank correlation coefficients. Results A total of 749 participants were included in the analysis of criterion-related validity between the CFS and HDS-R. In the CFS cohort analysis, 202 patients (27.0%) were categorized as having a normal CFS, and the median HDS-R score was 18 (range: 6–26). The correlation coefficient between the CFS and HDS-R scores was -0.834 (p < 0.001). The correlation coefficient between BR and BI was -0.741 (p < 0.001), BR and KI was -0.740 (p < 0.001). Conclusion The CFS revealed significant criterion-related validity compared with the established cognitive assessment scale, the HDS-R. The BR also demonstrated significant criterion-related validity with the BI and KI.