Faleh Almaleki is accused of killing his 20-year-old daughter in 2009 because he thought she was becoming too Westernized, KSAZ-TV, Phoenix, reported Monday.
The state's case could conclude as soon as Monday.
Before court adjourned last week, a witness testified she saw Almaleki's vehicle strike his daughter, Noor Almaleki, as she and the witness were walking in nearby Peoria, The Arizona Republic reported.
The daughter died about two weeks later.
Almaleki was charged with first-degree murder, attempted first-degree murder, aggravated assault and two counts of leaving the scene of a serious-injury accident.