Earlier this year, CNN executives floated an idea to their star anchor Chris Cuomo. If he wanted to formally advise his brother, Gov. Andrew M. Cuomo of New York, on responding to the sexual harassment accusations that had engulfed his administration, he could take a temporary leave from CNN and return to the network later.

The idea was informal and strictly optional — not a request — and intended as an acknowledgment of Mr. Cuomo’s unique position as both a prime-time network anchor and the brother of a prominent politician facing a scandal, according to two people who spoke on the condition of anonymity to describe internal conversations…

In private conversations this week, some CNN journalists expressed dismay to one another that Chris Cuomo did not address the story on his Tuesday program. Some argued that CNN should have disciplined him, according to several people with knowledge of internal discussions.

Those in-house critics would not speak on the record, for fear of antagonizing management. In May, the anchor Jake Tapper told The New York Times that Chris Cuomo’s engagement with Governor Cuomo’s aides “put us in a bad spot,” adding, “I cannot imagine a world in which anybody in journalism thinks that that was appropriate.”