Innocent Prey (1984)

A woman living in Dallas discovers that her husband, from New Zealand, is actually a crazed serial killer who murders prostitutes. She helps the authorities arrest him, and he is sent to a hospital for the criminally insane. Just when she's starting to get her life back together, she learns that he's escaped from the institution and is after her. She flees to Australia and winds up staying in a house owned by a wealthy young man, who turns out to have dark secrets of his own.