Electrical transport measurements through single InAs and CdSe semiconductor nanocrystals embedded in a thin polymer film were performed using conductance atomic force microscopy. The current and topography images showed excellent correlation, where current was detected only over the nanocrystals. A rapid current decay in consecutive scans was observed for positive sample bias, while remaining intact at negative bias. This current decay was accompanied by bias-dependent changes in the height of the nanocrystals. These phenomena, which were not observed for gold nanocrystals, are attributed to long-sustained charging of the nanocrystals.