Whose 501c do you use?

I was wondering:

When sponsors offer you money and their donations are tax-deductable, do you give them the SCHOOL’s 501c, or do you guys have your own? (I.e., are you a separate organization from your school?)

We use the schools.

I thought that PUBLIC schools could not have a 501… a specific school support group…but PTO, Boosters etc can.

We go through the Rochester Community Schools Foundation, a district-wide 501c.