Chicago (Author-Date) is one citation option in the Chicago Manual of Style. But it's slightly different than footnotes you may be used to seeing. Keep in mind
For an Authored Report from a Government Agency:
Bibliography:(B) Last Name, First Name. Year, Title. Report Number if Available. Publisher Location: Publisher. URL
In-text: (N): (Last Name, Year)
General Report by an Agency or Organization
B: Organization Name. Year. Title of Report. Place of Publication: Publisher. URL.
N: (Organization, Year)
More examples of grey literature like government reports or UN documents can be found at the the Naval Postgraduate School's Knox Library. All other types of sources should be checked in the Chicago Manual of Style.
In Zotero, which version of Chicago Manual of Style should you choose?
There are two main varieties of "Chicago style." Your instructor might want you to use the "Author-Date" system (more common in the sciences and social sciences) or the "Notes and Bibliography" system (more common in the arts and humanities). Read more on these two systems of citation from the Chicago Manual of Style, and check with your instructor or TA if you have any questions about which is appropriate for your paper.
If you are using the Author-Date system, choose "Chicago Manual of Style 17th edition (author-date)" from the Zotero document preferences menu.
If you are using the Notes and Bibliography system, you have two options in Zotero: (full note) or (note). Unless instructed otherwise, use the option labeled (full note). This will provide a full note the first time you cite a work, with a shortened note for subsequent citations. (Read more about short notes from the Chicago Manual of Style.) In some cases, you may want to choose the version labeled (note). This version uses the short citation format every time you cite a work in your paper, and is used for papers where the complete bibliographical information on your sources only appears in the full bibliography at the end. In either case, you have the option to display citations as footnotes (at the bottom of your page) or endnotes (at the end of your paper).