The claim says complacency by guards and medical staff resulted in the November 2011 death of 27-year-old Lyndsey Elizabeth Lason who had been arrested for investigation of theft and prostitution.
The Daily Herald reports Lason complained of trouble breathing for more than a week, and other inmates poked fun at her for the "eke, eke, eke" sounds she made when trying to inhale. She died of a pulmonary infection that filled her chest with pus.
"For whatever reason, she got infected and the infection was crushing her lungs," said attorney Royce Ferguson. "She literally suffocated to death over a period of 8 days, maybe 10 days."
According to the wrongful death claim filed against Snohomish County and the cities of Everett and Des Moines, Lason's breathing was noticeably labored.
Lason's cousin, Jennifer Taylor, said Lason repeatedly asked to go to the hospital and specifically asked for a chest x-ray.
"There were several requests and ongoing cries for help. They were ignored," Taylor said.
"This was complete egregious indifference to someone's calls for help. She would push the button, 'Help me, help me, help me,' and they would yell at her, 'Quit pushing the emergency button,' " Ferguson said.
A spokeswoman for the sheriff's office, Shari Ireton, says it can't comment on an active claim.
There have been seven deaths at the jail in Everett since 2010.