New York City police say they have a suspect in custody in the killing and dismembering of a 45-year-old woman.

The woman's body was found in heavy duty plastic garbage bags by a man walking his dog Tuesday morning. Police say the head was in one bag, a leg and arm in another and a torso in a third. The cause of death has not yet been determined.

Police say a man has made statements implicating himself in the crime. His name hasn't been released.

Police had cordoned off at least four separate locations on the streets surrounding the initial discovery.