The children were discovered after a gas explosion Wednesday at the town house, but are not thought to have died as a result of the blast. Riggi is hospitalized in serious but stable condition after apparently falling from an upper story of the house on the same day.
"Due to the medical condition of the accused, it is not at this time known when she will appear in court," a police spokesman said on condition of anonymity in line with policy.
Riggi and her husband, American oil industry executive Pasquale Riggi, 46, of Colorado, were getting divorced and contesting the custody of their children.
Scottish authorities said the couple were due to attend court hearings in the case this week, and on Tuesday a judge raised concerns over the children's safety when their mother failed to appear for the divorce proceedings.
Police said they are investigating the circumstances of the deaths and have interviewed the children's father, but confirmed he is not a suspect in the case.
They said the autopsies on the children were completed Friday. No details were disclosed, but a report has been submitted to prosecutors, police said.
Pasquale Riggi described his anguish over the death of his children.
"Our family is struggling to come to terms with the immense and tragic loss of three beautiful children," he said in a statement issued by Edinburgh's Lothian and Borders police department.
His wife and the children went missing from the family's home in Aberdeen, a port town about 100 miles (160 kilometers) north of Edinburgh, on July 21, prompting police to launch a search.
Pasquale Riggi grew up in Colorado, where he attended Denver's Regis Jesuit High School, graduating in 1982. He serves as an executive with Royal Dutch Shell PLC in Scotland, and had previously worked with the company in the Netherlands.
"The Huffington Post"
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