Senior Constable Jackie Fyfe was the first officer on the scene after the police car she was in was waved down on Favona Road in Mangere.
RNZ reports Gustav Otto Sanft is on trial in the High Court in Auckland for the manslaughter of his 2-year-old daughter, Amokura Daniels-Sanft.
Giving evidence, Ms Fyfe said she ran onto the driveway and heard a howl.
She said a man was holding a child with grievous head injuries.
Ms Fyfe said she needed to check for signs of life but the man would not put the child down.