The suit claims police didn't probe hard enough on Brian's side of the story ... and even claims the officers treated Brian as if he were the victim, rather than the perpetrator, of domestic violence.
In the family's eyes -- all signs pointed to Brian, and they say the cops "egregiously misinterpreted" the situation.
Her family also calls out the department for failing to train its cops for situations like this -- characterizing this case as a "vehicle for systemic change and a reckoning about how the police enforce the State's domestic abuse laws." They are seeking $50 million in damages.
The city of Moab tells TMZ ... "We feel profound sympathy for the Petito and Schmidt families and the painful loss they have endured. At the same time, it is clear that Moab City Police Department officers are not responsible for Gabrielle Petito’s eventual murder."
The city says it will defend itself against the suit.