Giving Up the Ghost — Marilyn Levinson

After her divorce, Gabbie Meyerson moves to the sleepy town of Chrissom Harbor, Long Island, to teach English at the local high school. She settles into her rental cottage above the Long Island Sound and discovers she has a housemate--the ghost of Cameron Leeds, who used to live in the cottage. Cam insists his death was no accident, and implores Gabbie to find out who murdered him eight months ago. After she recovers from her initial shock, Gabbie agrees to investigate.
She learns from CH residents that Cam was the town daredevil, romeo, and wheeler dealer. His four friends Reese, Jack, Terry, and Don are angry because Cam deceived them in a land deal. They each have a personal reason to hate him, as well. And his lover's husband is a possible suspect. Despite what she hears, Gabbie finds herself growing fond of Cam and continues to search for his killer.
At school, Gabbie has to contend with two bullies who pick on one of her students, but receives no support from the ineffectual principal. She becomes friendly with Cam's married lover, Jill Leverette, whose strange neighbor, Sonia Russell, has turned hostile, though Jill doesn't know why.
A mutual attraction springs up between Gabbie and Cam's best friend, Police Chief Darren Rollins, which she tries to ignore. After their first date, she decides it's time Darren reopened the investigation into the circumstances of Cam's death. She has Darren talk to Cam in his present form.
The investigation is opened, and someone attacks Gabbie inside the cottage. One of the bullies is murdered and the other goes missing. Nerves are on edge as town residents search for the boy. And suddenly the murderer's inside Gabbie's cottage, putting her life and the boy's in danger.