Police said Gotbaum, 45, was intoxicated and unruly after missing her connecting flight while on the way to a substance-abuse rehabilitation clinic in Tucson.
Maricopa County Attorney Andrew Thomas said officers didn't know Gotbaum suffered from alcoholism and depression.
"Mrs. Gotbaum's death, while tragic, does not warrant criminal charges against police officers who were simply trying to carry out their duties. They committed no crime," Thomas said.
The announcement didn't come as a surprise to the Gotbaum family's attorney, Michael Manning.
"We never believed that the officers intentionally killed her," Manning said. "From what we know at this stage, they may have been grossly negligent in how they treated her. But they certainly were not acting criminally."
Gotbaum's family has filed an $8 million lawsuit against the city of Phoenix and its police department.