If you are in a class or any of the following subjects are your major, you should probably use C/T format:
The most recent edition of this book is in the reference area on the 2nd floor of the library. While you can't check out reference items, you may be able to check out older editions of the book at the same call number on the 3rd floor.
You should use whichever one your professor requests, but in brief, the Chicago Manual of Style covers specifications to authors for preparing manuscripts for publication. Kate Turabian was the dissertations secretary at the University of Chicago graduate school for many years. She wrote her Manual for Writers of Research Papers, Dissertations, and Theses as an adaptation of the Chicago Style for graduate students. So, it follows the Chicago Style closely, but covers the unique needs of students writing formal papers.
---from the Marysville University guide