The United States possesses the technical means to determine the point of origin of a nuclear device, even one which has been detonated. Each reactor's output would leave a distinct signatureand if the weapon was from China, then that nation would have some serious explaining to do.
More likely than not the Chinese would stumble over themselves trying to prove that it wasn't one of their weapons, up to and including allowing the US to test weapons on site to remove any doubt of the weapon's origin. This is because while China has 300 or so nuclear weapons, the United States has thousands. It also possesses the conventional strike capability to severely degrade much of China's military infrastructure in response to such an attack.
North Korea or a stolen Pakistani nuke would be more likely culprits. Depending upon what the investigation turned up, anything from stringent sanctions to one or more heavy conventional military strikes would be the most likely response. In North Korea's case, this would probably be followed by the toppling of their civilian leadership.
China has ballistic missiles, so if it wanted to start World War III, it has more efficient means to do so that using a smuggled nuke. It would also fare the worst in any nuclear exchange at this point making it exceptionally unlike that it would foment one.