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If the church is licensed as a school, there is nothing that turns that designation off on Sundays (or Saturdays, either). That the building is currently being used as a church and not a school doesn't fly when congregations hold their services at the local elementary school building. I can't see it working in your favor here.

The law makes it clear that carrying on the premises of a school is illegal. Yes, you might be safe under the "portion of a building" reference, but what church school doesn't use the auditorium for chapel, plays, graduation, etc. If the school uses that portion of the building, even irregularly, I would say that carry is off-limits. If I were in your shoes (and I am not a lawyer, so this is only my opinion of what the law says), I would leave the CCW at home or in the car. I wish I had a better answer for you.