That's correct, Robert, but Crosley did build one in-dasher for its cars, the 1939-1942 Roamio. Sales of these were very low, perhaps because they added measurably to the cars' FOB prices.
The early CCs have Zenith 5MX080 radios, which are very similar to those in contemporary Fords. In fact, they even have some rudimentary motor-dial chassis equipment.
By 1948-1949 and thereafter, Crosley's radio supplier became Motorola with its CY8.
The rule of thumb to discern the Zenith and Motorola radios at first glance is to study their dial lettering (although this isn't infallible because I've seen several variations.) The Zenith dials usually use finer Roman serif lettering while the Motorolas usually use the heavier slanted Crosley font lettering.