SHANGHAI, April 6 (Reuters) - China’s blue-chip index retreated on Tuesday, pressured by healthcare and consumer companies, as upbeat economic data raised worries of policy tightening. ** The blue-chip CSI300 index fell 0.4% to 5,140.34, while the Shanghai Composite Index was flat at 3,482.97. ** As of last close, the CSI300 had rebounded nearly 6% from a recent trough hit on March 25, while SSEC had gained more than 4% in the same period. ** Falling the most on Tuesday, the CSI300 healthcare index and CSI300 consumer discretionary index dropped 1.7% and 1.6%, respectively. ** Recent economic data has been robust, but analysts warn that it could lead to concerns of inflation and policy tightening. ** A recovery in China’s services sector picked up speed in March as firms hired more workers and business optimism surged, although inflationary pressures remained, a private sector survey showed. ** The Caixin/Markit services Purchasing Managers’ Index (PMI) rose to 54.3, its highest since December, and well above the 50-mark that separates growth from contraction on a monthly basis. ** If China’s inflation and GDP growth data, due later this month, beat expectations, policy tightening worries will be kindled, Huaan Securities said in a report. ** Analysts said foreign investors becoming net sellers via the Stock Connect last week weighed on short-term sentiment and as the issuance of new mutual funds slowed substantially. ** Around the region, MSCI’s Asia ex-Japan stock index was firmer by 0.33%, while Japan’s Nikkei index closed down 1.3%. ** At 07:07 GMT, the yuan was quoted at 6.552 per U.S. dollar, 0.24% firmer than the previous close of 6.5675. ** As of 07:08 GMT, China’s A-shares were trading at a premium of 33.19% over the Hong Kong-listed H-shares. (Reporting by Shanghai Newsroom; Editing by Rashmi Aich)