Miss Marple: A Caribbean Mystery (1989)

Feeling poorly, Miss Marple's nephew sends her to Barbados for a bit of a holiday. She finds the holiday a bit of a bore and nowhere near as interesting as life in St. Mary Mead. Things get a bit more interesting when one of the guests, the elderly Major Palgrave, is found dead. The death is put down to natural causes until one of the maids finds medication belonging to another guest in the late major's room. When the maid is also found dead it is clear that the Major's oft-repeated tale of knowing a murderer - he was in the colonial police after leaving the army - convinces Miss Marple that the murderer is someone at the hotel.