Can one task be associated with multiple projects in Time Doctor?

Yes.

You can associate the same task name with multiple projects. In this case, each task will be treated as a separate instance of that task and time will not be tracked cumulatively across all projects. This means that you can have the same task name for one or more projects.

For example, you have two projects:
1. Daily
2. Important

And you have a single, common task,  emails, that you want to use for both projects.

You can create permanent tasks for your two projects in the Projects and Permanent Tasks page.

Both tasks now have a bracket with the name of the project next to the task name.

The Project Report page will now look like this: