David Perry, a family spokesman, said her family were "stunned" and were enduring a "nightmare".
The hospital and sheriff's department conducted a search of the premises and Ms Spalding's friends and relatives spent days scouring the streets of the California city with flyers.
They said they were "under the assumption San Francisco General had been searched."
Mr Perry said: "Lynne Spalding died alone, in the stairwell, at one of the finest medical institutions in this country.
"I hear that the San Francisco Sheriff's Department initiated a search. Well, evidently it wasn't a very good one. I think there are a lot of questions to be asked."
More top news
Vera Robinson MBE has died at the age of 101. She had been a fundraiser for the Redcar RNLI lifeboat station since she was 16 years old.
Provisional statistics for July show it was a cool and wet month for many of us.
With just 49 days until the start of the Rugby World Cup, the Webb Ellis Cup is touring our region.