Yes, the build record for your car will have the engine number for the
engine originally installed in your car. (Not sure when they stopped doing
it - would be after 1957, though.)
The engine number on your car would be stamped on the left side of the
block, at the front. The prefix for a 1938 Chrysler Imperial engine would
be C19, and would run from C19-1001 to C19-9172.
Bill
Vancouver, BC