Considering this patient did not present with any symptoms of pain, and in fact came for routine evaluation of another medical problem, denotes chronic nature of the displacement of the IUD into the peritoneal cavity. 

Normally a radiograph or even a sonogram suffices to identify an IUD which is in situ, displaced within the uterus, embedded in the wall. It gets harder to identify in sonography the peritoneal IUD, while frontal and lateral radiographs will give a clue. 

Encounters of IUD in CT is limited to incidental findings when being evaluated for other issues. However, CT is the modality of choice to understand complications that could arise from displacement or migration of the IUD - pelvic inflammatory disease, pelvic adhesions, abscess, hollow visceral perforation, etc.