In Europe, the only country where water deer have been recorded free-range, to my knowledge, is France. Based on accounts by Kenneth Whitehead, in his 1993 Whitehead Encyclopedia of Deer, and a paper to the Monthly Bulletin of the National Hunting Office in France during in November 1995 by Eric Sand and François Klein, three animals were introduced to Parc de Ligaure, owned by the Department of the Haute-Vienne, near Limoges in France, during in 1954 and lived there for several decades. A few escaped in the early 1960s and this appears to have been the nucleus for a wild population in the region. This population was supplemented by escapees between 1965 and 1970 as the park was gradually abandoned and the fences fell into disrepair. According to John Long, in his Introduced Mammals of the World, there were also some deliberate releases:
“Between 1960 and 1965 some Chinese water deer were released for sporting purposes near Solignac-leUgen, south of Limoges. Here they became well established and a few years later one was killed 80 km to the south-west.”
By 1974, the water deer was a protected species in France and hunting it in the region was subject to prosecution by the police.
In their 2017 review of the water deer, Ann-Marie Schilling and Gertrud Rössner give three locations for current free-range populations of water deer in France: around Limoges, just east of Châteauroux, and just south of Vannes. According to Christine Saint Andrieux, Project Manager on the team responsible for monitoring wild ungulate populations at the National Hunting and Wildlife Agency (Office National de la Chasse et de la Faune Sauvage), this is not the case, however. In 1991, Chinese water deer were present in the wild in France in and around two communes of the Haute-Vienne: St Jean de Ligoure and Le Vigean. There is no current monitoring, but there have been no confirmed reports of individuals in the wild for at least the past ten years and, in September 2016, Christine Andrieux told me: “The two last surveys of exotic ungulates (2006 and 2013) did not show any Hydropotes in the wild living in France.”
There is some evidence to suggest that the increase in the water deer population in South Korea has resulted in its spread north within its historical range throughout the Korean peninsula, resulting in some individuals crossing the China-Russia border. The earliest of which I'm aware was a buck shot in January 2014 in Russia's Mikhaylovsky District, just north of Vladivostok. The hunter provided photos, two of which were published by Dmitry Belyaev and Yeong-Seok Jo in their 2021 paper to Mammalia. Unfortunately, while the deer in the photos is unquestionably a mature water deer, we only have the hunter's word, and no verification was provided, so it remains a viable but anecdotal report. In their 2019 Russian paper to Заповедная наука (Nature Conservation Research), Yury Darman and colleagues also recount anecdotal reports, dating back to 2015, by border guards who described “marsh musk deer” in the Hasan district of Russia. More recently, remote cameras have picked up water deer making the crossing.
In their paper, Darman and his team wrote that shortly after 4am on 1st April 2019, a camera trap set in the Land of the Leopard national park captured a photo of a water deer - the first verified sighting of the species in Russia. Subsequently, in late May 2019, a buck was observed crossing the Tumannaya river from North Korea into China's Hunchun State Nature Reserve. A few weeks later, during early July, a buck was hit by a car near Jeansin village in China, only four kilometres (2.5 miles) from the Russian border.
In a Russian paper to Vestnik IrGSHA in 2021, Belyaev and colleagues recounted two further verified reports of water deer killed by hunters near the city of Ussuriysk, also in the Mikhaylovsky District. One individual was a female killed accidentally by hunters targeting roe deer in November 2020 in the Ozernaya valley, close to where the buck was shot in 2014. Later in the same month, a buck was filmed running around the city centre in Ussuriysk by a member of the public and posted to social media. The buck became stuck in a fence near the Moskva shopping centre. Unfortunately, the animal was killed by stray dogs after having been freed, but the carcass was sent for analysis and confirmed the buck was roughly two years old, in good condition and weighing 18 kg (40 lbs). In their paper the authors suggest the buck was driven into the city from the city from the floodplain of the Rakovka or Komarovka rivers following freezing rain that reduced available food. Whatever the source, these data suggest the water deer is more widely distributed in Russia than previously thought, and the authors consider it likely that there is now an established population.
In the discussion of deer introduced to Australia in his 1978 book, Arthur Bentley references the “paddyfield deer”, which he suggests are most likely water deer. According to Bentley, a pair were breeding at Royal Park in Adelaide, south Australia, during 1868 having been introduced the year before, but they appear to have remained within the confines of the park. Bentley also mentions rumours that these paddyfield deer had become established along some sections of the south Australian coast, including one about a ship carrying water deer that was wrecked off Yorke Peninsula. The animals were alleged to have been released, or had otherwise found their way ashore, and they took up residence in a difficult swampy region on the peninsula. Assuming this to be true, the population apparently didn't persist and the Feral deer management strategy 2010–2015 and 2013-2018 make no reference to water deer, suggesting they are no longer present in Australia.
Finally, some ranches in the USA, particularly Texas, hold water deer, but my understanding is that availability is limited, and most stalkers/hunters travel to Britain. I'm not aware of any living wild in the country.