I don't have a definitive answer, but looking inside the code of bootci.m (by using edit bootci), I see enough usage of norminv and normcdf to guess that it is assuming normal.
That being said, I did not carefully step through the code to understand it. I will say that there are more-than-usual references inside the code, to the paper DiCiccio, Thomas J., and Bradley Efron. “Bootstrap Confidence Intervals.” Statistical Science 11, no. 3 (1996): 189–228. (This reference is given in the documentation.) So, to be really confident, I think you'd need to understand that reference.