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Theoretically, CME kinematics are related to magnetic reconnection processes in the solar corona. However, the current quantitative understanding of this relationship is based on the analysis of only a handful of events. Here we report a statistical study of 60 CME-flare events from August 2010 to December 2013. We investigate kinematic properties of CMEs and magnetic reconnection in the low corona during the early phase of the eruptions, by combining limb observations from STEREO with simultaneous on-disk views from SDO. For a subset of 42 events with reconnection rate evaluated by the magnetic fluxes swept by the flare ribbons on the solar disk observed from SDO, we find a strong correlation between the peak CME acceleration and the peak reconnection rate. Also, the maximum velocities of relatively fast CMEs (> 600 km/s) are positively correlated with the reconnection flux, but no such correlation is found for slow CMEs. A time-lagged correlation analysis suggests that the distribution of the time lag of CME acceleration relative to reconnection rate exhibits three peaks, approximately 10 minutes apart, and on average, acceleration-lead events have smaller reconnection rates. We further compare the CME total mechanical energy with the estimated energy in the current sheet. The comparison suggests that, for small-flare events, reconnection in the current sheet alone is insufficient to fuel CMEs. Results from this study suggest that flare reconnection may dominate the acceleration of fast CMEs, but for events of slow CMEs and weak reconnection, other mechanisms may be more important.