There should be a serial number on the butt of the grip frame; you may have to remove the grips or stocks to see it. A few prewar S&Ws have the serial on the frontstrap under the trigger guard, but most of these guns are .22LR, .32 Long, or .38 S&W rather than .38Spl.
If the number on the butt has been removed- which is possible- the cylinder serial number may be repeated on the underside of the barrel above the ejector rod.
It is also helpful to know (a) how many rounds it holds, as the different frame sizes used to have overlapping serial number ranges, (b) if there is an alphabetical prefix such as "S" or "C", and (c) if there is a model number inside the yoke cut, the part of the frame that becomes visible with the cylinder open.
You've posted that you have a .38 Special revolver, probably Smith & Wesson, and added a possible serial number.
It could be a number of possibilities.
CTG is cartridge, not a model.
