Ms Petito’s parents Joe Petito and Nichole Schmidt also accuse Chris and Roberta Laundrie of planning to help Brian leave the country in the lawsuit, which was first reported by WFLA.
Chris and Roberta Laundrie have described the allegations as “baseless” in a statement released by their attorney Steve Bertolino to The Sun.
The suit contains new claims that have never previously been revealed by the FBI.
Ms Petito’s body was found in the Grand Teton National Park in Wyoming on 19 September.
Her cause of death was given as “manual strangulation”.
The lawsuit alleges Ms Petito’s body also showed signs of blunt force trauma to her head and neck.
In a note found near Laundrie’s remains in the Myakkahatchee Creek Environmental Park, on 20 October, he claimed responsibility for her murder.
The FBI concluded that her boyfriend Brian Laundrie murdered her by manual strangulation.
The FBI said he had claimed responsibility for his girlfriend’s murder in a note found near his body.