Brand, Christianna - Green for Danger (1944)

Source: Wikipedia

The book was praised for its clever plot, interesting characters, and wartime hospital setting. A 1946 film version was made, starring Alastair Sim and Trevor Howard, with Sally Gray and Rosamund John. It was directed by Sidney Gilliat and is regarded by film historians as one of the greatest screen adapations of a Golden Age mystery novel.

A murder takes place in a rural British hospital. Inspector Cockrill is tasked to determine whodunit when the head nurse is killed after revealing that the death of a patient under anesthesia was no accident. Cockrill states at one point, "My presence lay over the hospital like a pall - I found it all tremendously enjoyable". After another murder attempt leaves a nurse dangerously ill he re-stages the operation in order to unmask the murderer.

See also: http://onlydetect.wordpress.com/2011/01/25/christianna-brand-green-for-danger-1944/

and: http://crimepieces.wordpress.com/2012/07/03/classic-crime-christianna-brand-green-for-danger/

There is also a book of this title by Holt, Gavin