UPDATE: Jonah Shacknai released a statement with ex-wife Dina Romano announcing that their son Max died in the hospital Sunday. A full story will follow.

Rumors that Jonah Shacknai's 6-year old son, Max, died on Saturday are not true, but speculation persists that the boy may be brain dead and on life support.

Last week, the son of the millionaire Medecis Pharmaceuticals CEO suffered serious injuries after falling down the stairs in Shacknai's Coronado mansion, known as Spreckles Mansion - the same home where Shacknai's 32-year old girlfriend was found dead on Wednesday, hanging from a rope dangling over a courtyard.

Coronado police spokeswoman Lea Corbin told The Arizona Republic that Max Shacknai was in fact still alive, but offered no insight into how critical his condition may be. The child is alive and has not passed. I don't have any information (on his medical condition). I just know he has not passed.

No law enforcement official or medical authority has confirmed or denied rumors that Max is brain dead and/or on life support.

On Saturday, multiple media outlets quoted a Facebook message posted by Max's older sister, indicating that her brother had died.

RIP Maxie. We'll miss your sweet smile and kind heart more than you'll ever know. I'll love you forever, San Diego's Channel 8 news reported the message read. 

IBTimes was not able to locate the message on Facebook today; and it appears that Gabriele Shacknai's profile may have been removed altogether.

Corbin also told the newspaper that there does not appear to be any connection between Max Shaknai's injury and the bizarre death of Jonah Shacknai's girlfriend, Rebecca Nalepa (also known as Rebecca Zahau).

It just seems to be a tragic accident, she said.

Rebecca Nalepa's dead body was found nude, bound, and hanging from the mansion's balcony on Wednesday.

Jonah's brother Adam Shacknai made the discovery, and told police that he cut Nalepa down after finding her. Both her ankles and wrists were bound.

This is a very bizarre death, there's no doubt about it, San Diego Sheriff's Capt. Tim Curran told reporters.

There are some very unique ways people can take their own lives, Curran added. If it was determined to be a suicide, people will do some very bizarre things.

Mary Zahau-Loehner spoke to ABC News about her sister Rebecca's state of mind before the gruesome discovery, saying that when the sisters spoke on Tuesday night, things with Rebecca did not seem out of the ordinary.

She was normal, fine, just getting ready to go to bed, Zahau-Loehner said.

On Monday, Max Shracknai suffered a fall down a staircase in the home, and was not responsive when the paramedics arrived.

The boy had fallen from stairs and was not breathing and did not have a pulse, Coronado Police Chief Louis Scanlon said Thursday. As of that day, the boy was in critical condition.

At this time, we have no information that would lead us to believe this is anything other than a tragic accident with the child, Scanlon added.

A San Diego kennel owner who spoke to Nalepa on Tuesday said the woman was shaken by the recent events at her home.

It is believed that Jonah Shacknai was not home during his son's injury nor when Rebecca's body was found.

There has been no explanation yet from the medical examiner's office about how Nalepa might have hung herself while her wrists and ankles were bound; nor has there been any information disclosed about the material used to bind them.

Land records show that Shacknai, 54, whose Scottsdale, Arizona-based company is the maker of the acne treatment Solodyn and wrinkle-filler Restylane, purchased the 27-room landmark property known as the Spreckels Mansion in October 2010.

From 1977 to 1982, Shacknai served as chief aide to the House of Representatives committee with responsibility for health policy, and in other senior legislative positions.

He was also a member of the Commission on the Federal Drug Approval Process, and the National Council on Drugs.

On Thursday, Medicis had its sharpest decline in stock price since February.

Police have sealed all evidence related to the case, including search warrants and Nalepa's autopsy report.