The Cat Wears a Noose — Dolores Hitchens

A drunken man is shot dead on his doorstep in this classic mystery starring the “observant [and] appealing” seventy-year-old sleuth (Publishers Weekly).
 
Walking home wearily from an evening spent poring over the books of the Parchly Heights Methodist Ladies' Aid searching for a fifty-eight-cent error, Miss Jennifer Murdock becomes witness to a terrible scene: A man, stumbling drunk, arrives home -- and just as he fumbles with his keys, gunfire erupts and kills him on the spot.
 
Jennifer is determined not to tell her sister, Rachel, anything about it. After all, Rachel considers herself a sleuth, or as Jennifer views it, a busybody who pokes her nose in places it doesn't belong. What she doesn't know is Rachel has just had a visit from a member of that same household, a meek eighteen-year-old taken in after she was orphaned and treated like a servant. Young Shirley has been alarmed by a series of nasty pranks -- and now she's heartbroken, and even more frightened, after finding her pet bird dead. There's something awful going on in the house on Chestnut Street, and neither her prim and proper sister nor Det. Lt. Stephen Mayhew can stop Rachel from finding out what it is . . .
 
“Rachel has never yet failed to solve a murder mystery. Never before have her methods been quite so devious and unorthodox as they are in this story.” -- The New York Times
 
The Cat Wears a Noose was previously published under the pseudonymD.B. Olsen