Indian and non-Indian children who are not eligible for enrollment in Bureau-operated schools under § 31.1 may be enrolled in such schools under the following conditions:

(a) In boarding schools upon payment of tuition fees, which shall not exceed the per capita cost of maintenance in the school attended, when their presence will not exclude Indian pupils eligible under § 31.1.

(b) In day schools in areas where there are no other adequate free school facilities available, tuition fees may be charged for such enrollment at the discretion of the superintendent or other officer in charge provided such fees shall not exceed the tuition fees allowed or charged by the State or county in which such school is located for the children admitted in the public schools of such State or county.