AS3 startDrag/stopDrag is similar to AS2 except it uses mouse events to detect the mouse movement, below is a simple implementation:

package {

    import flash.display.*;
    import flash.events.*;

    public class DragExample extends Sprite {

         function DragExample() {
                 addEventListener(MouseEventType.MOUSE_DOWN, onMouseDown);
                 stage.addEventListener(MouseEventType.MOUSE_UP, onMouseUp);
         }

         private function onMouseDown(event:Event):Void {
                 this.startDrag();
         }

         private function onMouseUp(event:Event):Void {
                 this.stopDrag();
         }
    }
}

You will need stage to listen to mouse up event in order to stop dragging as you might release your mouse too quick or not on the sprite.