You can use the Win32API SendMessage function to send messages to window objects from TestComplete. Please see the following example that demonstrates how you can use the SendMessage function:
' Run Windows Calculator
Call Win32API.WinExec("calc", SW_SHOW)
Set p = Sys.Process("calc")
Set w = p.Window("SciCalc")
' Send the WM_CLOSE message to the Sys.Process("calc").Window("SciCalc") window
' WM_CLOSE = 16
Call Win32API.SendMessage(w.Handle, 16, 0, 0)
Please pay attention to the fact that not all messages can be sent between different processes (e.g. between TestComplete and your application).
So in case you cannot send the desired message directly from TestComplete, you can try to create an auxiliary OLE object accessible from TestComplete scripts. Using this approach you can pass the desired message along with its parameters to this OLE object via its methods. This object in turn will send the message to the destination control.