I am guessing that since he has an LD you get it written into an IEP for him and since you are providing the funding for the tutor you may be able to get the school to agree to it. Schools usually require any adults working with the students to go through a background check of some sort, often times it includes fingerprinting, sometimes it is simply scanning their drivers license and checking it that way.
It sounds like a good plan, good luck with it.