Did you get a good look at the dresser the day it happened? Does it appear that the dresser, in fact, DID fall? The items on the dresser would have been moved, maybe a few broken or chipped, and the dust patterns around the items on the dresser would have been disturbed. The contents in the drawers would have been messed up, and if you have deep pile carpet you should see where the dresser had moved slightly from the original position.
The bruise on the child will look different. A fist makes a fist shaped round bruise, a dresser would make one with more straight line geometrics, and she'd likely have other bruising or tenderness on her back, back of her head, etc, where she fell back against the floor.
Well, kids do sometimes lie to avoid getting into trouble, no doubt about it. Problem is, there really is no way to know for sure and well, this is your child. So many kids are harmed by a mothers boyfriend or new husband. I think it happens a whole lot more then people realize.
My personal opinion is that you have to react. You just do. Either something is actually going on, or your daughter is having challenges accepting him as her step dad for some other reason, and either scenario does not make for a happy household. I can only tell you what I would do (or at least think I would do). I would ask your fiance to leave the house for a short time at the very least. I would then spend a whole bunch of one on one time with your daughter getting to the bottom of it. Be careful not to lead her or put words in her mouth, but talk to her. It may very well be she is just resentful of this man and new baby taking mom's time from her and this is how she is handling it. Or, you may come to the conclusion he really did hurt her. Again, this is only my opinion and what I believe I would do if faced with the same situation. Not easy I'm sure, and I wish all of you all the best.