The victim, a fourth-grade primary school student aged under 12, managed to unlock an Ofo bike on March 26 and was riding along with friends before being struck and run over by a bus,
according to Chinese media reports. The child died after being taken to hospital.
Following an investigation, local traffic police determined that the child was riding down the wrong side of the road and bore "primary responsibility" for the accident, the reports said.
Chinese traffic regulations stipulate that children must be at least 12 years old to ride bicycles on public roads.
But through their lawyer, Zhang Qianlin, the family said Ofo should bear responsibility given its bikes were unsupervised and readily available in public spaces and that its bike locks were inadequate, given the victim and three other underage companions were able to unlock and use the bikes.
The bikes posed a "great hidden risk to safety", the family said, the state-run China Youth Daily reported on Saturday.
There have been at least two deaths and more than 10 injuries involving children riding Ofo bikes, the report said, raising questions over increased government scrutiny and regulation in the fast-evolving market.