This is a novel by Josephine Tey. According to the review,
"It is the story of Alan Grant, a policeman with Scotland Yard, who is laid up in the hospital after being injured on the job. A friend brings in a portrait of Richard III and he has a hard time believing that the man in the picture is the horrible, nephew murdering hunchback that he is familiar with. This sparks his interest and to relieve his boredom he takes up the 400+ year old case of Richard III - did he or did he not murder his nephews in the Tower? He and an American researcher working in the British Museum sort through all the evidence they can get and look at the case through a policeman's perspective - considering motives, opportunities, written accounts from the times, looking for breaks in the normal routine of the main players, etc. Grant becomes convinced that, based on the evidence, that Richard did not murder his nephews. In fact, he had absolutely nothing to gain and quite a bit to loose if he did."