Erica Flores, 22, died when her car was hit by a South Bend police car near the intersection of Western and Kaley last July.
A grand jury decided not to indict Officer Justin Gorny, but he was fired by the department.
In the wrongful death lawsuit, the family claims the city failed to train Gorny how to properly operate his patrol car as speeds over 50 miles an hour.
It also claims Gorny was negligent, reckless and violated department policy.
The family is seeking unspecified damages.