Use SendMessage to send the WM_NCLBUTTONDOWN in the HTCAPTION area.
Code:
Private Declare Function SendMessage _
 Lib "user32" Alias "SendMessageA" ( _
 ByVal hwnd As Long, _
 ByVal wMsg As Long, _
 ByVal wParam As Long, _
 lParam As Any) As Long

Private Declare Function ReleaseCapture _
 Lib "user32" () As Long

Private Const WM_NCLBUTTONDOWN = &HA1
Private Const HTCAPTION = 2

Private Sub Form_MouseDown(Button As Integer, Shift As Integer, X As Single, Y As Single)
    If (Button And vbLeftButton) = vbLeftButton Then
        ReleaseCapture
        SendMessage Me.hwnd, WM_NCLBUTTONDOWN, HTCAPTION, ByVal 0&
    End If
End Sub
Good luck!