As other's have mentioned, laws vary from state to state, and can be confusing. In regards to autism spectrum disorder, in my state (MA), there may not be any restriction on a school psychologist diagnosing ASD (other than general guidelines about not doing things you're not qualified to do). I know several school psychologists who conduct ASD evals. However, the state law mandating insurance coverage for autism requires that the diagnosis be made by a "licensed physician" or "licensed psychologist", and in this state "licensed psychologist" and "licensed school psychologist" are different things- the former requires a doctoral degree. The ASD diagnosis by a the school psychologist may qualify the student for special education services, but an insurance company will not accept it as proof of diagnosis- they will require it form a psychologist or physician.
Across the border in the state of CT (less than 10 miles/16 km from my office), a licensed clinical social worker also can give a qualifying diagnosis for insurance funded treatment. These differing regulations can be very confusing for practitioners, as well as put families in a bind when they move from one state to the next and are looking for services for their child.