Laser speckle contrast imaging (LSCI) has classically been used to image regional blood flow changes in animal models. In this paper, we demonstrate the use of LSCI for elucidating blood flow characteristics in individual microvessels with diameters as small as 24µm. We extracted profiles of speckle contrast values within individual vessels, both along their diameters and along their lengths and inferred that they could be attributed to the flow within the vessel. Profiles along the diameter of vessels revealed maxima at the center of vessels, consistent with fluid dynamics. These observed profiles could be fitted with parabolic curves with a mean coefficient of determination of 0.92. Similarly, analysis of speckle contrast values in the axial direction revealed profiles that progressively decreased in discreet quanta at branch points indicating blood flow bifurcations. Flow estimates obtained from speckle contrast values within branches of vessels obeyed the law of mass conservation with a mean error of only 3.5%. This allowed us to elucidate the percentage distribution of blood flow into each of the downstream branches. This ability of LSCI to resolve blood flow distribution in branching microvessel trees in a minimally invasive and dye free environment over a wide field of view promises to find application in both the neuroscience laboratory as well as intraoperative neurosurgery.