The claim, the legally required precursor to a lawsuit, seeks $8 million for Gotbaum's husband, Noah Gotbaum, her three children and her estate.
"On that day, members of the Phoenix Police Department used excessive and unreasonable force on Carol, as if she was a dangerous criminal, rather than as the sick, intoxicated and vulnerable person she was," the claim states.
Gotbaum family attorney Michael Manning went on to write that police erred by putting her alone and shackled in a holding room.
"In the process, they ignored the warning signs that their own policies, procedures and training materials told them could result in Carol's death," Manning wrote.
An autopsy concluded Gotbaum accidentally hanged herself on her shackles while in the room. Gotbaum's husband is the son of New York Public Advocate Betsy Gotbaum.
Police have contended that Gotbaum's death was accidental and that officers who took her into custody did nothing wrong.
But lawyers for her family have accused police of mistreating her and then leaving her unattended in the holding room.
An autopsy report released by the Maricopa County medical examiner's office concluded that the hanging death was accidental and called intoxication on alcohol and prescription drugs contributing factors.
Manning has acknowledged that Gotbaum "drank excessively at the airport."
Wednesday's letter from the city's legal department to Manning said the claim that police should have responded differently was wrong.
"The thrust of the Gotbaum family claim is that the City of Phoenix police officers should have been more supportive than Carol's own husband, more knowledgeable than her own family, and should somehow have known that she suffered from a private condition that she deliberately hid from the public," said the letter signed by Stephen Craig, a lawyer for Phoenix. "But the Gotbaum family has publicly admitted, not only that Carol hid her medical and mental condition, but that the officers responded to Carol exactly the way her husband knew they would respond because they did not have critical information known only to the Gotbaum family."
The city letter included transcripts of phone calls Noah Gotbaum made to the airport the afternoon of his wife's death, telling officials he was concerned about her whereabouts because she was depressed and suicidal.
