This study examined the association between finger tapping and cognitive function in a group of 225 elderly participants (116 males; age 79–92 years; M = 82.5; SD = 2.4). Finger tapping was assessed in two conditions: self-selected pace and fast pace. Based on cognitive assessments, including the MoCA and CERA-NP test battery, participants were classified as cognitively healthy individuals (CHI), participants with mild cognitive impairments (MCI), and those with possible MCI (pMCI). Results of the analyses show significant differences between groups, sex and the group × sex interaction in four parameters for the self-selected pace condition and eight parameters for the fast pace condition. These parameters were used for classification by means of linear discriminant analysis (LDA). The first LDA component showed significant differences between CHI and pMCI and between CHI and MCI. Furthermore, the second LDA component showed significant differences between CHI and pMCI as well as between pMCI and MCI. Nevertheless, the algorithm correctly classified only 50% of participants, regardless of group, suggesting that tapping parameters are only partially useful for classification in early stages of dementia. We discuss these findings in terms of the diadochokinetic nature of finger tapping as associated with the age-related degeneration of cortical and subcortical motor areas.