The Notorious Landlady (1962)

When William Gridley arrives from the US in London, he rents part of Carly Hardwicke's house from her and promptly begins to fall in love. Gridley doesn't know that many people think she killed her husband but his boss, the American ambassador, knows and doesn't take this "lapse of judgement" lightly. Since Carly is also American, Gridley saves his job by introducing her to the ambassador, who is promptly smitten and promises to help her. So when a Scotland Yard detective arrives, wanting to get to the truth one way or another, they say they'll help him. And then the comedic complications really begin.