You can send objects from Maya to Mudbox using the Send to options available from the File menu. The Send to workflow also allows you to send objects from Mudbox to Maya using the Send to options available from that application.

You must have both Maya and Mudbox installed on your computer; however, only one application needs to be open in order for the Send to workflow to work. For example, if you are sending objects from Maya to Mudbox, if Mudbox is not open, it will automatically launch once the Send to workflow is initiated.

For information on the Send to workflow, see Sending Objects to Mudbox.