Are crnas obligated to practice under supervision of an anesthesiologist?

No: They must work under a physician....Not necessarily an anesthesiologist.

Not always: In some states, the governor has chosen to "opt out" of the medicare requirement for nurse anesthetists to be supervised by an anesthesiologist or by any other physician. In other states, physician supervision is required by law. The anesthesia care team, where a nurse anesthetist is supervised by an anesthesiologist, is widely used as a model of very safe and cost-effective anesthesia care.

Usually...: It depends on where you practice. CRNAs are usually required to practice under the supervision of an anesthesiologist. They can also practice under the supervision of the surgeon.