What article in the NEC allows home owners to wire their own homes and is it only their residents and not their rental?

Deciding who is allowed to do electrical work is not discussed inside the NEC. That is the function if the Local Authority Having Jurisdiction.

For example, here in Virginia, a home owner can pull an electrical permit and do the work on his/her home.

Commercial permits are only issued to licensed electricans. Rental poroperty requires a licensed electrican.

Don is correct... in NJ it's contained in the NJ Uniform Construction Code

Same for GA. BUT make sure you do it right. Get a code book.