Earlier they had interviewed Amy’s friend, Ashley, and her mother Debbie Rose, who were the last people to see the 15-year-old before she disappeared on New Year’s Day.
The police took away Amy’s computer from the family’s apartment and hope to discover if she had been in contact with a paedophile or anybody she could have gone away with.
The interviews were part of the continuing police investigation into what happened Amy, now missing for more than 11 days.
Her mother, Audrey, and her mother’s partner, Dave Mahon, were invited to come to the Guardia Civil Station in Fuengirola to help their inquiries yesterday evening.
Afterwards they refused to answer questions put by journalists waiting outside and rushed to their car.
However their spokesman, Franco Rey, read out a statement confirming they were interviewed twice yesterday.
“They are doing everything they can to assist the Guardia Civil in building up a picture of Amy’s whole life and piece together her movements over the past few days.
“Discussions with the police in an investigation are a police matter and it is not for the family to reveal what has been said”.
Earlier Ashley, 13, was questioned about what the girls did on the day Amy went missing when they were babysitting Audrey’s three-year-old brother Jake.
There has been some criticism of Ms Rose for allowing Amy to walk home alone at 10 o’clock at night and yesterday she said she felt guilty about this now but she had no car at the time.
“I have children of my own that are my responsibility and Amy was her family’s responsibility. They were at home that night and they never rang to offer her a lift home,” she said.
Amy had been walking home alone at night for the past two years and Ms Rose said she never remembered her family ringing to offer her a lift in that time.
“She has been tempting fate for a long time, especially with a lunatic out there,” she said, referring to reports that a man in the area had been offering lifts to young girls.
The police have said they are keeping an open mind on the case and are investigating a number of scenarios, including that Amy ran away, that she has been kidnapped or that she has been murdered.
Her father, Christopher Fitzpatrick, flew to Malaga during the week with his sister Christine Kenny. Amy was due to go to Dublin to visit him after Christmas and was upset when the trip was cancelled. It’s not known if the police will question him.
Spanish police have also asked the gardaí, through Interpol, to assist in the investigation by checking if Amy could have returned to Ireland. She did not, however, have a passport.
A two-day search earlier in the week of a 6km area around her home in Calahonda on the Costa del Sol by more than 200 police, Red Cross, sniffer dogs and two helicopters failed to turn up any clues as to what happened the girl.