Though they are the most abundant stars in the Galaxy, M dwarfs form only a small subset of known stars hosting exoplanets with measured radii and masses. In this paper, we analyze the mass-radius (M-R) relationship of planets around M dwarfs using M-R measurements for 24 exoplanets. In particular, we apply both parametric and nonparametric models and compare the two different fitting methods. We also use these methods to compare the results of the M dwarf M-R relationship with that from the Kepler sample. Using the nonparametric method, we find that the predicted masses for the smallest and largest planets around M dwarfs are smaller than similar fits to the Kepler data, but that the distribution of masses for 3 R ⊕ planets does not substantially differ between the two data sets. With future additions to the M dwarf M-R relation from the Transiting Exoplanet Survey Satellite and instruments like the Habitable Zone Planet Finder, we will be able to characterize these differences in more detail. We release a publicly available Python code called MRExo (https://github.com/shbhuk/mrexo) that uses the nonparametric algorithm introduced by Ning et al. to fit the M-R relationship. Such a nonparametric fit does not assume an underlying power-law fit to the measurements and hence can be used to fit an M-R relationship that is less biased than a power law. In addition, MRExo offers a tool to predict mass from radius posteriors, and vice versa.