Normally if someone dies while in the custody of police there is automatically an inquest as to what happened. If there's evidence of mistreatment or abuse, the District Attorney can then decide to send the case to a grand jury and let them decide whether they should charge the officers involved. The DA can also indict and charge the officers without a grand jury. In most cases, DA's send their cases to the grand jury in effect to "test" how strong the evidence is they have.
In the Ferguson case, the grand jury waded through thousands of documents and decided the conflicting witnesses testimonies and physical evidence made them decide not to indict officer Wilson for the shooting.
Even if the DA decides not to prosecute (for whatever reason), then the family can hire an attorney and file a wrongful death case (violation of constitutional rights) as a civil suit against the city. Civil cases also have a lot lower burden of proof or what we call "the preponderance of the evidence" meaning its more likely something than not something happened.