I could not find any information to support either way. Can female dwellers give birth to twins? If so, what are the odds of this happening?
There is no argument to support either way. That said, it is more likely not possible. If it was, it would at least be touched on, across the guides, the wikias etc.
That said, it is possible to have twin dwellers, as experienced by a user at this Reddit post. The user reports having received identical dweller cards from lunchboxes, and it was unrelated to breeding.
I only wanted to add this screencap as a reply to a comment, but I don't have the reputation. So I'll abuse the system with an "answer" that isn't that much of an answer.
My Ms Bowman had two sets of twins prior to the triplets shown below, with Roxy equipped before and throughout the pregnancy with Three Dog as the father. FWIW, they are my two most charismatic dwellers, and spend most of their time together in the radio room.
This is in an obviously small vault, on iOS. I've had less luck with Roxy in a larger PC vault, perhaps one set of twins out of 10 pregnancies.