* HSI -0.7 pct, H-shares -0.8 pct, CSI300 +0.5 pct
* China c.bank unveils policies to support property sector
* HSBC PMI falls from 17-month high in September
* Hong Kong down on weak overseas markets
By Chen Yixin and Kazunori Takada
SHANGHAI, Oct 8 (Reuters) - China shares nudged higher on Wednesday, with a key index hitting a 20-month high, supported by strength in property developers after the central bank rolled out policies to boost the struggling sector.
The Shanghai Composite Index rose 0.3 percent to 2,370.86 points by midday, its highest since February 2013, as Chinese market resumed trade after a week-long holiday. The CSI300 of the leading Shanghai and Shenzhen A-share listings gained 0.5 percent.
In Hong Kong, sentiment was dampened by global markets. The Hang Seng Index fell 0.7 percent to 23,253.06 points by midday while the China Enterprises Index of the top Chinese listings in Hong Kong was off 0.8 percent
"The latest property policy had some impact on the performance of the sector today," said Du Changchun, analyst at Northeast Securities in Shanghai, referring to China's real estate sector.
However, he said gains were being capped as any policy impact was unlikely to be immediately reflected on an economic level.
The People's Bank of China on Sept. 30 cut mortgage rates and downpayment levels for some home buyers for the first time since the 2008-09 global financial crisis, making one of its biggest moves this year to boost an economy increasingly threatened by a sagging housing market.
The property sub-index of the CSI300 jumped 1.8 percent, with Hua Yuan Property surging by its 10 percent daily limit and China's largest residential developer China Vanke rising 2.4 percent.
Some heavyweight shares, such as oil and financials, fell due to worries over the economy after China's HSBC services PMI index fell from a 17-month high in September.
"The downtrend in these shares indicates the market is still not optimistic on the economic outlook," said Du.
Hong Kong shares surrendered all of its gains from the previous day after overseas markets posted sharp losses in the wake of the International Monetary Fund (IMF) cutting its global economic growth forecast.
The IMF on Tuesday cut its global economic growth forecasts for the third time this year, suggesting the environment remains difficult for companies, especially ones with multinational exposure.
Some blue chips were among the biggest drags on the Hong Kong indexes, with Tencent Holdings Ltd dropping 1 percent and China Mobile Ltd falling 0.7 percent.
"The sharp losses in U.S. stocks weighed heavily on the Hong Kong market today, but I believe it is about to rebound soon due to certain positive factors, including the upcoming Hong Kong-Shanghai trading connector," said Ying Hao, an analyst at Yuanta Securities in Shanghai, referring to the cross border trading scheme. (Additional reporting by Shanghai Newroom; Editing by Jacqueline Wong)