The Thursday Murder Club (Thursday Murder Club 01) by Richard Osman

Four residents of a very nice retirement village enjoy discussing unsolved crimes. They have quite the unofficial paper database because their former fourth of the club was Peggy, who is now comatose and has been replaced by Joyce, as the fourth club member. But Peggy's dear and devoted friend, Elizabeth, still has access to those files and makes good use of them.
Enter a real live (or maybe the word dead should be used) crime when a developer for nearby properties is found murdered! The foursome had already taken a shine to a young female cop named Donna, who had given them a talk on the fine points of crime (which most of the group already understood). Add in Donna's lonesome, dedicated, boss, Chris and you have two groups, official and unofficial, trying to solve this crime. Pull the thread of one body and more bodies start dropping, present and past. What more fun could a geriatric crime solving club want, although things get personal and sad when it all hits too close to home.