Code Editor doesn’t have any Dropbox support at this time.
We would like to add protocol support for Dropbox in a future update. What would this mean? You’d be able to authorize Dropbox as a server type and edit files on it as you would any other web server in Code Editor. We do not have an ETA for this at this time.
If this is critical to your workflow, you can use a third party service called DropDAV. It allows you to connect to your Dropbox account via WebDAV, which Code Editor supports. This will also work for Transmit Mac, Transmit iOS and Coda 2 for Mac. The service is $5/month, but it works really well. Note: DropDAV is not affiliated with Panic in any way.
Dropbox for local files
As of Code Editor 2.0, we no longer support Dropbox for local files, as Code Editor has its own storage capability. At this time, we do not have plans to bring this back, as protocol support (as mentioned above) takes care of this.