BEIJING, June 2 (Reuters) - China shares fell on Wednesday, as investors booked profits after a rally in consumer and healthcare firms following the country’s latest three-child policy. ** The bluechip CSI300 index fell 0.95% to 5290.86 at the end of the morning session, while the benchmark Shanghai Composite Index lost 0.65% to 3601.24. ** Falling the most, the CSI300 consumer staples sector and healthcare subindex skid 1.15% and 1.35%, respectively. ** The two sectors, including some birth- and fertility-related companies, were cheered by investors on Tuesday after Beijing allowed married couples to have up to three children, as recent data showed a dramatic decline in births in the world’s most populous country. ** The pullback in stocks also came amid a northbound outflows via the Stock Connect, hitting 3.6 billion yuan ($564.15 million) on Wednesday, according to Refinitiv data. ** Shenzhen’s start-up board ChiNext slipped 1.56%, while Shanghai’s tech-focused STAR50 index was down 1.56%. ** The smaller Shenzhen index was down 0.95%. ** Chinese H-shares listed in Hong Kong fell 0.42% to 10,945.09, while the Hang Seng Index was down 0.5% at 29,320.10. ** Around the region, MSCI’s Asia ex-Japan stock index was weaker by 0.21% while Japan’s Nikkei index was up 0.44%. $1 = 6.3813 yuan Reporting by Beijing Newsroom; Editing by Rashmi Aich Our Standards: The Thomson Reuters Trust Principles.