The lawsuit filed Thursday accuses 25-year-old Dwight L. Smith Jr. of reckless and wanton conduct in striking 65-year-old Marsha Lee with an SUV in December 2011. Authorities have said that after hitting Lee with the vehicle, Smith threw her inside, raped her and beat her to death.
Smith once wrote that he might have become "addicted to killing people" while serving in Iraq and Afghanistan. His family has suggested that he has post-traumatic stress disorder.
Smith was examined over five days last month at the Delaware Psychiatric Center, but results of the psychological testing are sealed. He has not yet been returned to prison.