The University of Alabama and the sheriff's office mishandled Megan Rondini's case, her parents say.
Ms Rondini, then a 20-year-old student, claimed she was sexually assaulted by a local man at his home in July 2015.
The lawsuit claims police treated her as a crime suspect instead of a victim and the school failed to support her.
According to the lawsuit, Ms Rondini met Terry Bunn Jr at a popular Tuscaloosa bar and was sexually assaulted and possibly drugged at his home.
Mr Bunn, who maintained the encounter was consensual, was not charged.
Upon leaving Mr Bunn's house, Ms Rondini said she took his gun to protect herself and $3 from his wallet to pay for a taxi home.
Her parents claim police wrongly focused on her actions after the incident and were sympathetic towards Mr Bunn, whose family owns a local construction company.
Cindy and Michael Rondini allege that Mr Bunn evaded prosecution because of his family's local prominence.
Cindy Rondini told CBS News on Wednesday she drove from Texas to Alabama after the incident to comfort her daughter, who said she felt that police thought she was at fault.
"It was the most heartbreaking moment of my life," Mrs Rondini said.
"Megan ultimately was treated as a crime suspect and her status as a victim of a sex crime was completely disregarded," the lawsuit contends.
The 25-page legal action, filed on Monday, names Mr Bunn, the Tuscaloosa County sheriff, a sheriff's deputy, a sheriff's office investigator and two university employees.
It claims the sheriff's office did not take Megan Rondini's claims seriously and the university failed to give her adequate psychological treatment and support.
Ms Rondini left the university and returned home to Austin, Texas, where she suffered depression, anxiety and post-traumatic stress disorder, directly leading to her suicide, say her parents.
She hanged herself shortly after transferring to a college in Texas in February 2016.
The university told CBS News that school officials "handled their responsibilities with care at all times keeping Megan's wellbeing as their absolute highest priority".
Mr Bunn's lawyer denied the accusation in a statement.
"The allegations against my client as set forth in this baseless lawsuit are simply false," said the attorney, W Ivey Gilmore. "No sexual assault occurred."
The Rondinis say any money won in the lawsuit would be donated to groups to support rape victims.
Her case was raised last week on the floor of Congress.
Texas Republican Ted Poe, chairman of the Congressional Victims' Rights Caucus, said Ms Rondini "got the death penalty" after investigators treated her "with disdain and disbelief".

Pallas's cats are found in Iran, Mongolia and China.
David Barclay, of the Royal Zoological Society of Scotland (RZSS), has been in contact with a researcher in Iran since 2013.
In a new development, an abandoned Pallas's cat kitten could be radio-collared for the first time in Iran.
Efforts to capture images of the animals in Iran using camera traps have been unsuccessful so far.
Mr Barclay said putting a radio collar on a young cat and releasing it back into the wild could help uncover new information on the cats.
He said: "Should this happen we will be in a position to offer financial support and gain a valuable insight into the behaviour and ecology of Pallas's cats in their western range."
RZSS is also supporting a new Pallas's cat research project in the central Alborz Mountains of Iran.
Mr Barclay said: "It is clear that interest in the species is growing not just in range countries but throughout the zoo world.
"It is an exciting time for Pallas's cats and as long as I am breathing I will continue to support the conservation and research efforts and wave the Pallas's cat flag."
RZSS has Pallas's cats in its collection at its Highland Wildlife Park at Kincraig near Aviemore.
They are also known as Manul, steppe and rock wildcat.
They are classed as "near-threatened", according to the International Union for Conservation of Nature and Natural Resources.
The break up of their habitats are one of the biggest threats to the species.
The parents of an Alabama student who killed herself after claiming she was raped have sued her alleged attacker and local officials for wrongful death.
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Wild cat experts from Scotland are working with counterparts in the Middle East to better understand one of the world's rarest and most elusive cats.