Well, yes, at least for MN MA:

Eligible Providers (eligible to bill for testing (neuropsych testing has separate criteria)

• Licensed psychologists (LP) with competence in psychological testing

Mental health practitioner working as a clinical psychology trainee under the clinical supervision of a LP

• Psychological technicians, psychometrists or psychological assistants may administer or score psychological tests under clinical supervision of a LP.


And: 

Mental Health Practitioners Who Are Qualified as Clinical Trainees

A mental health practitioner working as a clinical trainee must meet the following:

  • • Be complying with requirements for licensure or board certification as a mental health professional including supervised practice in the delivery of mental health services for the treatment of mental illness
  • • Be a student in a bona fide field placement or internship under a program leading to completion of the requirements for licensure as a mental health professional

  • Medicare has separate guidelines, but specifically excludes supervisees who are "interns." 


    Commercial plans may allow billing for testing under supervision - you would need to check with your plans.