Currently this isn't possible to do nicely. I have some suggestions:
You can force the dropdown to be open anywhere in your app with
C1DropDownControl1.OpenDropDown()
The drop down is a form itself, so you can manipulate it's visibility with its Show method. But you'll have to play around with it to do what you want.
Private Sub CustomDropDown_VisibleChanged(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles MyBase.VisibleChanged
Me.Show()
End Sub
Regards,
Greg