A spokeswoman for the Massachusetts Office of Chief Medical Examiner told local media that the findings of cause and manner of death were pending.
Ms Rooney, who lived in Milton, Mass., worked in Dublin at one time with law firm Arthur Cox for four years.
The 80-year-old Ambassador, who is also owner of the Pittsburg Steelers was forced to fly home on Monday.
Her death is the second tragedy for Mr Rooney and his wife Patricia. The couple also lost their daughter Kathleen when she was just 31-years-old.
She was credited as the driving force behind her father's interest in tracing the Rooney ancestry to Co Mayo.
Mr Rooney will spend the rest of the week at least in the US dealing with arrangements for his daughter's funeral.
It means he will be unavailable to assist US Secretary of State Hillary Clinton on her visit to Dublin, which is due to start tomorrow.
She is visiting as part of a ministerial meeting of the Organisation for Security and Co-Operation in Europe.
Rita Rooney graduated with a degree in electrical engineering in 1980 and earned her law degree at the University of Pittsburgh in 1983. She served as a law clerk to a US District Judge in Maryland for about a year before joining Arthur Cox.
She later worked as a patent attorney with law firm Cesari & McKenna in Boston.
She most recently served as director of faith information at St Elizabeth Parish in Milton and was working on a Master's Degree in theology. She also taught religious education.
Parish priest Fr Aidan Walsh said: "She was a very creative woman, a very gentle person, easy to approach."