Inspector Rice (The Third Floor Flat)

In the short story The Third Floor Flat, Inspector Rice was the policeman who investigated the murder of Ernestine Grant which took place in the building Poirot lived in. He knew or had heard of Poirot, and, when he arrived on the scene of crime, greet Poirot in "an almost reverential manner".

There are two Inspector Rice in the Christie canon but they are unlikely to be the same person.