Depends. If the sleep disorder is something organic like sleep apnea or snoring, go to an MD who specializes in physical sleep disorders. If your sleep loss is caused by racing thoughts or anxiety/emotional issues, seek a psychologist (either PhD or PsyD) to help with issues of emotional regulation, with a possible consult to an MD psychiatrist for psychotropic med management for anxiety/sleep loss.
Sleep Specialist. American academy of sleep medicine requires an md who has completed residency training in medicine, pulmonology, ent, pediatrics, psychiatry, neurology and who have completed one year of additional sleep fellowship can take the exam and get certified i dont believe phd's are eligible to take the new board certification exam.
Both. Sleep disorders is a broad field and both md and phd are involved in the diagnosis and treatment of the diseases.. Dentists are also involved.