There is no time frame if there is no bail. They can place a "material witness hold" that requires very low standards of proof to hold a witness they say might leave the jurisdiction; flight risk - and it carries has no bail. They are not charging them with a crime, they are claiming that this person has vital information and their testimony is crucial to another case altogether.
https://www.inmateaid.com/ask-the-inmate/how-long-can-they-hold-an-inmate-without-the-inmate-being-indicted.amp#answer
Accepted Answer Date Created: August 05,2016