Multiple sclerosis (MS) is a neuroinflammatory disease that affects millions of people worldwide. Since dysarthria is prominent in people with MS (pwMS), this paper aims to identify acoustic features that differ between people with MS and healthy controls (HC). Additionally, we develop automatic classification methods to distinguish between pwMS and HC. In this work, we present a new dataset of a German-speaking cohort which contains 39 patients with low disability of relapsing MS and 16 HC. Findings suggest that certain interpretable speech features could be useful in diagnosing MS, and that machine learning methods could potentially support fast and unobtrusive screening in clinical practice. The study emphasises the importance of analysing free speech compared to read speech.