Linguistic alterations represent one of the prodromal signs of cognitive decline associated with Dementia. In recent years, a growing body of work has been devoted to the development of algorithms for the automatic linguistic analysis of both oral and written texts, for diagnostic purposes. The extraction of Digital Linguistic Biomarkers from patients’ verbal productions can indeed provide a rapid, ecological, and cost-effective system for large-scale screening of the pathology. This article contributes to the ongoing research in the field by exploring a traditionally less studied aspect of language in Dementia, namely the rhythmic characteristics of speech. In particular, the paper focuses on the automatic detection of rhythmic features in Italian-connected speech. A landmark-based system was developed and evaluated to segment the speech flow into vocalic and consonantal intervals and to calculate several rhythmic metrics. Additionally, the reliability of these metrics in identifying Mild Cognitive Impairment and Dementia patients was tested.