In the Cut (2003)

Frankie Avery is a NYC teacher who embarks on a relationship with NYPD Detective Malloy, who, along with his partner, is investigating the murder of a young woman, part of whose body was found in the garden outside of Frannie's apartment. Malloy believes this murder is the work of a serial killer. Beyond the murder investigation, she continues her association with Malloy despite her catching him in a lie which may have dangerous implications. As the relationship contributes, she discovers more evidence pointing to him being the serial killer.