Early postwar?? It's amazing that rear fender survived all that time without getting any dents. And no rack to protect it. That girl must never have let any boys ride her bike! Gary
If you flip the bike over you should find a serial number ending in 53Cw. The badge is a one year (1953) item used on the top of the line CWC Roadmaster Luxury Liners.
As a luxury liner the bike would have been fully equipped with a tank, rack, and the ball headlight with the big boxed fin. The hole in the top of the rear fender is evidence of the original rack which was braced to the rear fender (CWC typically used two rear fender braces on bikes that were not rack-equipped).
Of what remains, the springer and chain guard are original and the rear fender looks correct although it would have originally been chrome. The seat has been replaced as the original would have had deeper springs and the front fender is a replacement.
Here is a similar and complete (but slightly earlier) version of the Luxury Liner that recently sold on eBay.