We have developed a vector Doppler system based on an array transducer using a clinical ultrasound scanner with a research interface. In this system, vector Doppler is performed by splitting the array transducer into transmit and receives sub-apertures, which are then steered to obtain velocity estimates at different Doppler angles. The goal of this study was to characterize the size of the overlap region between the transmit and receive beams in both axial and lateral directions. We studied the effect of vector Doppler geometry, beam steering angle, aperture size and the depth of focus on the size of beam overlap region. Our results show that change in these parameters has minimal effect on the axial widths when a single transmit beam and two steered receive beams are used. However, the lateral widths tend to decrease with depth under all the factors under consideration. The average deviation of the beam widths was about 7% and 17% along the axial and lateral directions respectively over all 48 scenarios under consideration. Preliminary experiments on tissue did not substantially affect the beam overlap region.