There have been a number of theoretical and computational models which state that magnetic fields play an important role in the process of star formation. Competing theories instead postulate that it is turbulence which is dominant and magnetic fields are weak. The recent installation of a polarimetry system at the Submillimeter Array (SMA) has enabled us to conduct observations that could potentially distinguish between the two theories. Some of the nearby low mass star forming regions show hour-glass shaped magnetic field structures that are consistent with theoretical models in which the magnetic field plays a dominant role. However, there are other similar regions where no significant polarization is detected. Future polarimetry observations made by the Submillimeter Array should be able to increase the sample of observed regions. These measurements will allow us to address observationally the important question of the role of magnetic fields and/or turbulence in the process of star formation.