This thesis presents the results of a survey of 913 M-dwarf stars from the Lepine and Shara Proper Motion (LSPM) catalog within 33 parsecs. Data for these targets was collected with the Robo-AO camera on the Palomar 60” telescope. In order to determine which stars were in bound systems, the images with multiple stars, first observed in 2012, were observed again in 2014 to examine changes in separation and position angles. Stars with little change in position with respect to one another suggest they are common proper motion pairs. The Washington Double Star (WDS) catalog and other resources were used to further determine binarity. This research was conducted to improve upon the statistics of nearby multiple M-dwarf systems. Identifying and confirming multiple systems at both wide and small separations will improve our understanding of M-dwarf formation by comparing these results to existing star formation models.