The two men refused to speak to reporters as they arrived at the building in Almada, across the River Tagus from the Portuguese capital, to be questioned by a prosecutor behind closed doors.
The pilot and instructor could be charged following the interview, with legal experts speculating on a possible charge of negligent homicide. It carries a prison sentence of up to 16 years.
Terrified sunbathers ran for their lives, some of them into the sea, as the plane flew onto Sao Joao da Caparica beach yesterday after having mechanical trouble.
"The plane first hit the man, who had his back to it. Immediately after it lifted up and when it descended again it hit the child's head," Filipe Janeira, 34, who was at the beach, told daily Jornal de Noticias.
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The girl was with her parents, who were unhurt, and was on her way to take a swim in when she was hit.
Beachgoers surrounded the plane after it came to a halt on the sand and confronted the two men inside.
"The girl's father and other people went to the plane and started hitting the rear," witness Celia Rocha told daily newspaper Correio da Manha.
The instructor and pilot were unhurt and were led away from the Cessna CS-AVA plane by police for questioning. They were not arrested.
The instructor could be heard telling a control tower that the plane had suffered engine failure and was going to make an emergency landing, according to a recording broadcast on Portuguese television.
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