CT imaging has no absolute contraindications. The relative contraindications are related to the radiation dosage. The CT scan tends to be a more tolerable imaging study for patients who are claustrophobic.
MRI is definitely contraindicated in any patient who may have a magnetic foreign body within the eye or orbit, patients with cardiac pacemakers, magnetic intracranial aneurysm clips, and cochlear implants. The safety of MRI for the fetus during pregnancy is not known. Consequently, first-trimester MRI studies should be avoided if possible.