Why did Caroline in the City air on NBC, despite being produced by CBS?

[TMC]

Why did Caroline in the City air on NBC, despite being produced by CBS?

CBS had a production subsidiary called CBS Productions that was designed to produce content in-house, as opposed to relying on outside studios. The goal was to drive down costs and show that the Tiffany Network could be self-sufficient and didn't need outside content. As your question correctly implies, the production company existed exclusively to create new CBS programming, and not programming on rival networks like NBC.

Caroline in the City was produced by CBS Productions, but the CBS television network itself declined to add the show to its programming schedule. Because CBS Productions thought it had a hit on its hands, it sought and obtained permission to shop the show to other networks, and NBC picked it up. It was the first time a CBS Productions show was made for a competitor, although today, this practice is far more common.

[icecream]

It used to be illegal for a network to air its own studio's shows.