Is there a way for Citoid to work with a local database so that it doesn't need to go through Zoltero.
Topic on Talk:Citoid
I think the correct answer is: "Yes – theoretically". I think you would have to re-write parts of the software (so it could find and understand your local database).
So, there is no database with citoid OR Zotero's translation-server. Both Zotero and citoid generate citations on the fly, by querying APIs (like crossref) and scraping metadata from websites.
You CAN use citoid locally without setting up a local Zotero translation-server instance. However, it won't work as well. Configuration options to use or not use zotero are in config.yaml