Common Ground. Ghost Detective Short Stories, #4

Life as a ghost can be a lonely existence and Robert counts himself lucky to have had Clothilde by his side for thirty years. They watch the seasons pass and the mourners weep. Other ghosts come and go as they deal with their unfinished business. When Clothilde makes quick friends with a new arrival, Robert marvels at seeing her laugh and behave like a teenager again - even if it means loneliness for him.
She deserves some happiness. But when a second girl arrives in their cemetery, a pattern emerges. Robert and Clothilde must once again apply their crime-solving skills to go after their new friends' murderer.