The American Association of Medical College has data on undergraduate institutions for medical school applicants (not the same as accepted students): https://www.aamc.org/download/321458/data/factstablea2-7.pdf
I can’t sort the data, but it looks like the top five schools are all public universities:
UCLA - 926 applicants
Florida - 839
Michigan - 776
Texas - 773
UC Berkeley - 741
The top five private colleges are (unless I missed one):
BYU - 430
Cornell - 424
Johns Hopkins - 401
Emory - 380
Washington University - 376