This is an interesting question (for those of us who think procedure is at least as interesting as substance).
I've never heard of a court taking up both civil and criminal matters in the same proceeding. It would require a painstaking attention to procedural and evidentiary differences by the court, and if a jury was involved it would be unimaginably complicated (think of how you would begin to instruct a jury that it has to apply a beyond a reasonable doubt standard, and then forget about that and apply a preponderance of the evidence standard to the civil claim. Probably not worth the trouble.)
However, a habeus corpus proceeding is a civil lawsuit. I can at least imagine that this could be combined with a malicious prosecution, false imprisonment, or negligence claim. Or a civil rights claim. Why not?
Let us know what you find out.