Has she said her father's name is Harcourt Fenton Mudd? Perhaps Harry had an older brother.
I assumed when April mentioned her disreputable father that disreputable daddy was meant to be Harry Mudd. Yes, there's wiggle room in the intrepretation, but Orci did develop the story for this, and he does maintain that Admiral Archer mentioned in Trek XI is meant to be Jonathan Archer, so it wouldn't too much of a stretch to assume the intent was for the character to be the daughter of Harry Mudd.
Mr. Laser Beam wrote:
And we have no idea when first contact with the Bajorans took place. Thus it's not entirely unusual for Harry to have fathered a child by a Bajoran woman - in either timeline.
But, so far there's no reason why the character has to be Bajoran. She could easily be human with no changes to the story.