Topological Data Analysis (TDA) has increasingly gained recognition as a powerful and versatile mathematical framework aimed at extracting high-level structural features from complex datasets. Among the various tools that TDA offers, persistent homology has emerged as one of the most fundamental and widely adopted. However, clinical information is often presented in the form of time series. The present work focuses on applying TDA to data derived from continuous glucose monitoring (CGM) devices worn by diabetic patients. The study explores the potential of using persistent homology to transform CGM time series into meaningful topological summaries that may aid in distinguishing between patients diagnosed with Type 1 diabetes and those with Type 2. The experimental findings indicate that the exclusive reliance on topological information can discriminate between type 1 and type 2 diabetes patients. Nonetheless, the study is preliminary and limited to basic time series classification techniques.