The father, whom City Paper identified as Daniel Burch, did not return phone calls Thursday seeking comment.
Massey died at Children's Hospital of Philadelphia the evening of Sept. 25. Hospital officials declined to comment.
A letter sent home by the school Sept. 26 informed parents "of the sudden loss of a member of the Bryant . . . family."
The letter said the district's emergency-crisis response team would be at the school to provide counseling to children and staff.
"We all feel the loss of her presence, and our thoughts and prayers go out to her family," the letter said.
School District spokesman Fernando Gallard said that if the child had faced a medical emergency at school and said she could not breathe, Bryant officials would have called 911 instead of sending her home to her parents even if a nurse had been at the school.
Nurses "do not administer medical interventions," Gallard said.
He said he could not discuss Massey's health issues, but said the emergency occurred at her home - not at school.
"This is just tragic," said Jerry Jordan, president of the Philadelphia Federation of Teachers, which represents nurses.
A nurse would have known the child had asthma, understood the warning signs, and been able to assess her condition, he said.
"This is the tragedy we feared would happen when the Philadelphia School Reform Commission laid off about 100 nurses in 2011," Jordan said.
Inquirer staff writer Aubrey Whelan contributed to this article.