* SSEC -0.5 pct, CSI300 -0.8 pct, HSI -1.1 pct
* China c.bank doubles June liquidity injections to avert cash crunch
* Hong Kong blue-chips follow mainland lower
SHANGHAI, July 4 (Reuters) - China stocks fell on Tuesday morning, led by the blue-chip index losing ground for the third straight session following a strong rally on the back of its inclusion in a key MSCI index.
The CSI300 index fell 0.8 percent, to 3,620.69 points at the end of the morning session, while the Shanghai Composite Index lost 0.5 percent, to 3,180.03 points.
"The recent correction is technical as blue-chips had far outperformed the broader market this year, but we see little chances for a major downturn in industry-leading big-caps as they are not overvalued," said Xu Wei, an analyst with Hongxin Securities.
The robust trend in China's "nifty 50", the 50 most representative blue-chips in Shanghai, is broadening to the so-called "MSCI222", and investors could explore opportunities in blue-chips with solid fundamentals as rotation into those stocks is very prominent, Xu added.
U.S. index provider MSCI last month decided to add 222 China-listed stocks to its Emerging Markets Index, tracked by around $1.6 trillion.
The inclusion is widely expected to benefit the long-term development of China's stock market, in particular blue-chips.
Worries over tight liquidity conditions have eased after the mid-year macro-prudential assessment (MPA), although sellers have been pressuring Chinese markets over the past week or so on lingering fears of a cash crunch and slowing economic growth.
China's central bank injected a net 99.5 billion yuan ($14.64 billion) into the financial system via short-and medium-term liquidity tools in June, up 95 percent from the previous month, to ease tight cash conditions at the end of the quarter.
The central bank will hold off on further monetary policy tightening and could even slightly loosen its grip in coming months as a deleveraging drive threatens economic growth and job creation ahead of a leadership reshuffle, policy insiders said.
Sectors fell across the board in the morning, led by financials, and the defensive consumer and healthcare stocks.
Hong Kong stocks lagged the broader Asian markets, which rose on strength in Europe and the United States.
The Hang Seng index dropped 1.1 percent, to 25,497.94 points.
The Hong Kong China Enterprises Index lost 0.8 percent, to 10,333.25.
Most sectors lost ground, with heavyweight financials and other industry-leading companies mirroring a correction in mainland blue-chips. ($1 = 6.7974 Chinese yuan renminbi)
Reporting by Luoyan Liu and David Stanway