On reviewing the finished film, however, they found a deeper problem that “we didn’t have any way of seeing, or any way of fixing,” Mr. Cohen said: “White Westerners were saving China.” The picture was approved, he said, but its release was delayed until it had played elsewhere in the world, and pirated versions took a bite out of the Chinese box-office receipts.

For Americans, dealings with the Chinese censors are mostly a distant and secondhand business. Films are normally submitted by their Chinese partners, while various consultants in China handle the bureaucratic communications that lead to approval or rejection.

But those who shoot in China often assume that censorship officials have eyes and ears on the set. “There were points where we were shooting with a crew of 500 people,” said Mr. Cohen of his movie. “I’m not sure who was who or what, but knowing the way the system works, it’s completely clear that had we deviated from the script, it would not have gone unnoticed.”

In a 2011 Web post, Robert Cain, a producer and consultant who guides filmmakers through China’s system, described having worked in Shanghai on a romantic comedy that went off script; the director included a take in which an extra, holding a camcorder, pretended to be a theater patron taping a movie on a screen.

The next day, Mr. Cain and others involved with the film were summoned to the office of a Communist Party member who told them the film was being shut down for its “naïve” and “untruthful” portrayal of film piracy. Assuming they had been reported by a spy on their crew, the producers apologized and managed to keep the film on track.

Studios are seeking out official co-productions, in which a Chinese company works with an American studio in financing and creating a film, because they can bypass the Chinese quota system and bring their distributors a 43 percent share of ticket sales, rather than the 25 percent allotted to foreign-made films.

Co-productions like “Kung Fu Panda 3” draw close monitoring by the censors at every step. Scripts are submitted in advance. Representatives of S.A.R.F.T., according to Mr. Cohen and others, may be present on the set to guard against any deviation. And there is an unofficial expectation that the government’s approved version of the film will be seen both in China and elsewhere, though in practice it is not unusual for co-productions to slip through the system with differing versions, one for China, one for elsewhere in the world.