As far as I'm aware, the Chinese government as a whole has no official position on the origin of the virus. It is, however, possible to piece together a position based on local government actions, state media reporting, and actions of individuals within the government.
At the beginning of the outbreak, in January, a paper was published in the medical journal The Lancet by several Chinese medical professionals, which noted the outbreak, and found that 66% of infected patients had been in contact with a seafood market in Huanan. It also notes that "an epidemiological alert was released by the local health authority on Dec 31, 2019, and the market was shut down on Jan 1, 2020.", which shows that the local government at the very least was aware of the market being an infection vector, if not the initial origin of the disease.
However, a later report published in February by another team of Chinese scientists challenged this finding:
The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) was
instead imported from elsewhere, said researchers from Xishuangbanna
Tropical Botanical Garden under the Chinese Academy of Sciences and
the Chinese Institute for Brain Research.
The team, led by Dr Yu Wenbin, sequenced the genomic data of 93
SARS-CoV-2 samples provided by 12 countries in a bid to track down the
source of the infection and understand how it spreads.
What they found was that while the virus had spread rapidly within the
Huanan Seafood Wholesale Market in Wuhan, there had also been two
major population expansions on December 8 and January 6.
This later study was quickly picked up by Chinese state media - the Global Times reported its conclusions, as well as pointing out that other countries had reported multiple sources of infection:
Patients from Australia, France, Japan and the US - countries with
wider samples - have had at least two sources of infection, and the US
in particular has reported five sources, the study said.
In March, certain individuals within the government, most prominently Zhao Lijian, spokesman and deputy director-general of the Ministry of Foreign Affairs’ information department, made various accusations alleging that the virus originated within the US:
Zhao urged his more than 287,000 followers in two tweets on Friday
morning to widely share an allegation from a Canada-based conspiracy
website that the coronavirus – which has become a global pandemic –
originated in the US rather than the Wuhan seafood market that is
thought to be its source.
“This is so astonishing that it changed many things I used to believe
in,” he wrote on his official account.
A spokesman for the US embassy in Beijing declined to comment on
Zhao’s tweets.
The allegation was apparently linked to the US Army’s participation in
the international Military World Games held in Wuhan in October, which
drew competitors from more than 100 countries.
Over the last few weeks, as the international push for an investigation into the origins of the virus at the World Health Assembly increased, the Chinese government initially opposed an investigation into the origins of the virus, with Vice Foreign Minister Le Yucheng saying in an interview on April 30th that:
We are candid, and we are open. We support professional exchanges
between scientists, including exchanges for reviewing and summarizing
experiences. What we oppose, however, is unfounded charges against
China. One should not accuse China first and then run so-called
international investigations just to make up the evidence. This is
arbitrary investigation based on the presumption of guilt. That is
what we firmly oppose. As I said just now, the WHO-led expert group
visited Wuhan timely. As for the Wuhan Institute of Virology, it is
open to international communication. Ever since its establishment, it
has received visits by many international scientists, including those
from the United States. Just recently, the head of the Institute took
an interview with a foreign media, and made it clear that the
Institute has neither the intention nor the capacity to engineer any
kind of virus.
Interestingly, in the same interview, Le also tacitly acknowledged the Chinese government's involvement in the spread of the US military origin theory:
Janis Frayer: There have been some state media that have reported this
theory that the virus was actually linked to the US military. And this
is a theory that was amplified on social media by Chinese embassies,
some Chinese ambassadors. Is this an official Chinese position? If
not, why allow this disinformation?
Le Yucheng: Chinese government officials, the general public and
individual citizens are outraged as some US political figures are
using COVID-19 to slander China. They are entitled to express their
feelings, to question and rebut those slanders by various means. Here
in China, business leaders, customs officials and diplomats are
working so hard and around the clock these days to produce and pool
together supplies for COVID-19 response in the US. But what we have
heard all the time is bashing and slandering against China by some US
politicians. Try to put yourself in our shoes: how would you feel if
you were the Chinese people? Even worse, a Republican campaign memo
goes so far as to advise the candidates to address COVID-19 issues by
directly attacking China. Such flagrant moves have taken political
manipulation to a level beyond anyone's imagination. Of course the
Chinese people find them unacceptable, and have every right to express
their outrage.
Finally, at the 73rd World Health Assembly, President Xi gave a speech which has been reported as Xi supporting a "WHO Investigation Into Coronavirus Origins". Looking at the transcript of the speech, I'm not sure that it goes that far - the relevant part states:
China supports the idea of a comprehensive review of the global
response to COVID-19 after it is brought under control to sum up
experience and address deficiencies. This work should be based on
science and professionalism, led by WHO and conducted in an objective
and impartial manner.
It doesn't seem clear to me that a review of the global response would necessarily include an analysis of the origins of the virus, but that remains to be seen.
In conclusion, then, the Chinese government has not published an official position on what it believes the origin of the virus to be. Clearly, however, it acknowledges that Wuhan was a major hotspot - this is confirmed by the local government shutting down the Huanan seafood market and the quarantine that initiated in Wuhan. I'm not aware of there being any government position on the initial spread of the virus specifically being identified as from animal to human.
State media, and individual government officials, have supported claims that place the origin of the virus as outside of China, and central government has done little to inhibit the spread of this information.
The current position of the Chinese government appears to be that it will support an independent international investigation led by the WHO, but that now is not the right time - speaking to the BBC, Chen Wen, a Chinese diplomat said:
"We are fighting the virus at the moment, we are concentrating all our
efforts on fighting against the virus. Why talk about an investigation
into this? This will divert not only attention, it will divert
resources.
"This is a politically motivated initiative, I think no-one can agree
on this... It would serve nobody any good."