If the courts are giving you immunity, I think you have to have immunity from all levels of government. Otherwise your testimony at one level could incriminate

If the courts are giving you immunity, I think you have to have immunity from all levels of government. Otherwise your testimony at one level could incriminate you at another, right? I've never heard of this type of scenario, so maybe some precedent exists. Edit: why downvote? I'm generally curious about how they handle immunity with multiple levels of overlaping jurisdiction for most crimes.