We present the first in-depth statistical survey of flare source heights observed by RHESSI between March 2002 and March 2007, a total of 25,705 events. These flares were found using a new flare-finding algorithm designed to search the 6-12 keV count-rate when RHESSI's full sensitivity was available in order to find the smallest events. Thermal (4-10 keV) and nonthermal (15-25 keV) images were made for all microflares and source centroid locations were found for each event. In order to extract the height information from source positions, a Monte-Carlo model was developed with an assumed source height distribution where height is measured from the photosphere. We find that the best source height model is given by an exponential distribution with a scale height of 2.1 (0.3) Mm and a minimum height of 3.1 (0.3) Mm. Comparing with previously published loop length measurements, we find that the average loop tilt is ~44 degrees as measured from the vertical.