* HK->Shanghai Connect daily quota used -3.6%, Shanghai->HK daily quota used 1.9% * FTSE China A50 -1.7% SHANGHAI, April 9 (Reuters) - China and Hong Kong stocks fell on Friday, as robust inflation data raised worries over policy tightening and foreign selling via the Stock Connect pressured the A-share market. ** The CSI300 index fell 1.3% to 5,045.58 points at the end of the morning session, while the Shanghai Composite Index slipped 0.7% to 3,456.74 points. ** For the week, CSI300 dropped 2.2%, while the SSEC shed 0.8%. ** China’s factory gate prices rose at their fastest annual pace since July 2018 in March, official data showed on Friday, as growth in the world’s second-largest economy continued to gather momentum. ** Recent economic data has been robust, but analysts warn that it could lead to concerns of inflation and policy tightening. ** Leading the declines on Friday, the CSI300 transport index slumped 3.1%, as bellwether S.F. Holding Co Ltd tumbled after giving a bleak earnings estimate for the first quarter of 2021. ** Adding to the downbeat sentiment, foreign investors sold a net 2 billion yuan ($305.24 million) worth of A-shares via the Stock Connect linking mainland and Hong Kong on Friday, according to Refinitiv data. ** Their net buying in March totalled 18.7 billion yuan, down sharply from 41.2 billion yuan in February. ** Hopes of a strong U.S. economic recovery as Biden pushed forward with stimulus packages, lifted the dollar and the U.S. treasury yields, which could siphon away inflows into China, said Zheng Zichun, an analyst with AVIC Securities. ** “The northbound inflows into the A-share market could remain positive this year, but would probably slow,” he added. ** The Hang Seng index dropped 0.7% to 28,798.07 points, while the Hong Kong China Enterprises Index lost 1% at 10,997.24. ($1 = 6.5522 Chinese yuan renminbi) (Reporting by Luoyan Liu and Andrew Galbraith; Editing by Amy Caren Daniel)