I have an unpublished paper on this subject that sheds some light. I will summarize:
We have some interesting demographic data from the early 14th century in China showing the outbreak of various epidemics. These were very significant, and were certainly contributing factors to the demise of the Yuen dynasty. I say various because it is unclear from the documents whether the outbreaks were the same disease. Many of the surviving documents are brief, reporting only deaths.
So, we cannot say definitively whether the black death existed in China or not, but there was/were disease(s) at the right time, and it/they knocked out a significant chunk of the population.

EDIT: I realize this is ambiguous - the paper is not mine, my thesis advisor from grad school wrote it.

Follow up, why didn't the Black Death spread East, towards modern Korea and Japan?

A recent paper compared genetic divergence in various strains of Yersinia pestis with historical accounts in China and India. Some of their main findings are:

• Bubonic plague emerged in Asia and may have propagated along the Silk Road;

• While there are accounts of epidemics in China in the 14^th century, the state of the records does not allow to establish conclusively whether these were due to Y. pestis or not;

They also surmise that when the 14^th century epidemics hit, China and Europe may have been in different states of immunological readiness due to the probability of previous contact with the disease in it's pre-epidemic state in China, while Europeans were comparative "virgins" and much more vulnerable to such a newly introduced disease.

EDIT: typos

sorry if this seems a stupid question but...

If we have no records explicitly stating the Black Death affected China how can we say that it originated there?