Patients are often sedated for both CT scans and MRI, I am a previous RN who worked in radiology and I was responsible for either conscious sedation (primarily of children) or assisting the nurse anesthetist when the patient received general anesthesia. CT scan show structural abnormalities, MRIs do the same but are much more sensitive and are often used in seizure patients, patients with cancer, etc. When they are sedated, they are strapped in for safety.
Patients are never strapped in or sedated in a cat-scan because the straps may make the heart rate increase and cause anxiety and increased brain activity and sedatives kills brain activity. Doctors who preform these test are looking for anomalies at a resting or normal brain activity rate.