The lawsuit alleges police didn't do enough to protect their daughter from the man she had a restraining order against.
The Arizona Daily Star reports that the lawsuit was filed over the December 2012 of 23-year-old Ashley Hicks.
Police say Hicks was shot by 23-year-old Joseph Leroy Francis.
Francis drove to her parents' home in Marana and told them what he did.
The parents called Marana police.
Police later found Francis dead at his Tucson home.
The Tucson Police Department declined the newspaper's request for comment.
A message by The Associated Press for Tucson police wasn't immediately returned Thursday morning.