Can I sue the department of corrections for sending me back to jail After I was released?

The answer to the "can I sue" question is at most times, yes for anything, however, not always successfully.  Are you sure it was the Dept. of Corrections that sent you back to jail, from your facts, it sounds more like it was the police making possibly a false arrest or at least an arrest based on faulty information.  There is not much of a civil law suit in these facts.  It sounds like the DA was not able to make a case and thus you were not convicted or charged with the crime.  Your only damages would be the time in jail, and while that is important to you, it would rise to enough to bring a successful suit.  However, this is in the criminal law section, a penal civil rights attorney may have a different answer for you.