You'd have to say more about the setup. If you mean a dual-boot system, where only one OS is running at a time, you can share the data directory the same way you'd share any other files, though it's not impossible you'd run into trouble with one or the other operating system's support of the other filesystem and the standard filesystem mechanics required by SQLite.
You can of course always use Zotero syncing (set to download files "as needed", probably) to maintain separate versions of the database on each OS without sharing files.
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You can of course always use Zotero syncing (set to download files "as needed", probably) to maintain separate versions of the database on each OS without sharing files.