The Perennial Boarder — Phoebe Atwood Taylor

This time, Asey has to deal with a corpse that won't stay put. It all begins when Asey and Cousin Jenny encounter a woman in a terrible hurry in a hailstorm on the way to Quisset. Later that evening she turns up dead in a phone booth at the Whale Inn. When her body vanishes, reappears very much alive, and is finally, definitively pronounced dead on the porch of the Inn, Asey's grave doubts only multiply. Is this indeed the body of Miss Olive Beadle, the Inn's "perennial boarder?" Or isn't it?