The 375 Kansas City PD 4" Heavy Combat Masterpieces special ordered in April 1957 were in the K260XXX to K298000 s/n range with the lion's share K292XXX and were not model marked. However, there were subsequent (much smaller) orders placed by the KCPD so it's still possible the OP example could have been shipped to the KCPD. (note, during this timeframe, the KCPD typically refinished a duty revolver whenever it was returned to the armorer for service &/or re-issue. Given the amount of "refinishing" done to the OP's example, I suspect it went to the KCPD.

To help with terminology ... the factory (in general) referred to a 6" non-tapered barrel with wide barrel rib, adjustable rear sight and a Patridge front sight as a "K-38 Heavy Masterpiece" ... and anything less than 6" (e.g. 5", 4" or 2") non-tapered barrel with wide barrel rib, adjustable rear sight and a Baugman front sight as a "K-38 Combat Masterpiece".

Russ