You might find you need to have the same video in multiple projects. If this is the case you don't need to upload the video again. You can simply clone the video and then move it to it's new project.
Clone & Move
In this example I'm inside the Knowledge Base Videos project and I need to clone the video at the top. Just select it and then click on Clone:
Next click on the newly cloned video and then Move. A search field will appear where you can search for the destination project:
Once the correct project is found, click on the checkmark to save it:
At this point you may want to reset the analytics for the newly cloned video to start generating fresh data. Just follow these directions to reset analytics.