I found the following that seems to work. Is there another way of doing it that might be better?
Sub test()
 Dim oRng As Range
 Dim WrdInd As String
 Set oRng = Selection.Range
 oRng.Expand Unit:=wdParagraph
 Set oRng = ActiveDocument.Range( _
 Start:=oRng.Start, _
 End:=Selection.Start)
 WrdInd = oRng.ComputeStatistics(wdStatisticWords) + 1
End Sub