In a short statement issued on Friday, the family said the postmortem examination had confirmed that the death of Kennedy, aged 55, at home in Caol, near Fort William, on Monday "was a consequence of his battle with alcoholism".
After the family's postmortem statement was released, Conn O'Neill, who ran Kennedy's election campaign and became a close political adviser, said: "For just a year, I had the great honour of knowing Charles Kennedy.
A postmortem examination found that she had suffered blunt force trauma to the head, possibly caused by punches, and compression to the neck, either from a ligature or hands.
They are still trying to establish how and when the woman died, after an initial postmortem examination proved inconclusive.
A postmortem found that Marsden had died of "significant stab wounds" to the head and face.
We have found parts of bodies and biological matter that are currently undergoing postmortem examinations".
There will be a postmortem and we will issue a further statement when funeral arrangements are made".
A postmortem revealed she died from ventricular hypertrophy (thickening of the cardiac muscle of the heart) and obstructive sleep apnea due to morbid obesity, Hull coroner's court heard.
This may entail round-the-clock facilities in areas of minority concentration, and greater reliance on non-invasive techniques that might address cultural concerns about the prevalence and practice of postmortem.
The statement continued: "We have now been informed by the office of the procurator fiscal of the findings of the postmortem.
The statement said a postmortem examination had yet to be carried out.
