Detective Frank Minelli uses a synthetic eye. Presumably, it mimics the functions of a real eye, rather than just being cosmetic. When April opens Minelli's locker, she finds a case for the eye, suggesting it needs to be removed at intervals, like a contact lens.
However, the eye does have a disadvantage; it keeps coming out when Minelli sneezes. April replaces it with her Toy Monkey's Eye, which Minelli unwittingly puts back into place. However, given the iris of Constable Guybrush's eye is red, Minelli then thinks he's having a stroke.
Obtained from the shower room of the NPD station.