Letters of Recommendation for both the School AND the specific program of the school?

Is it normal to have your professor send letters of recommendation for admission into the school AND admission into the specific program (music in my case) for graduate study?

Check and see what the graduate school admissions office needs.
If he knows someone in the program and sends a LOR to that prof as well , it cant hurt.

The School admissions doesn’t need a LOR, but it has an option to include them if I want. Are you saying I might as well send them the same letters?

sue , it cant hurt .
include the LOR in your application.
It will be seen by the admissions committee, which may or may not include the prof.

If he/ she wants to put in his 2 cents re your application, he can do so to the admissions committee.