Gravitational microlensing can detect isolated stellar-mass black holes (BHs), which are believed to be the dominant form of Galactic BHs according to population synthesis models. Previous searches for BH events in microlensing data focused on long-timescale events with significant microlensing parallax detections. Here we show that, although BH events preferentially have long timescales, the microlensing parallax amplitudes are so small that in most cases the parallax signals cannot be detected statistically significantly. We then identify OGLE-2006-BLG-044 to be a candidate BH event because of its long timescale and small microlensing parallax. Our findings have implications to future BH searches in microlensing data.