Police in the central Chinese city of Changsha said they were investigating personnel of GlaxoSmithKline (China) Investment Co., said the statement, which was reported by state media today.
Hong Kong's South China Morning Post newspaper on Monday said police had detained company employees in three cities: Changsha, the commercial hub Shanghai and Beijing.
A spokeswoman for the company, which has its China headquarters in Shanghai, declined to comment, saying she was not authorised to speak to overseas media.
The allegations involve at least one foreign executive employed by the company, said the postings on China's Twitter-like microblogs.
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The exact nature of the allegations was not specified by Changsha police. But authorities typically use the phrase "economic crimes" when referring to corruption.
It is common practice for Chinese pharmaceutical firms to offer doctors and hospitals bribes to have their products used, industry insiders say.
GSK is one of the largest multinational pharmaceutical companies in China with total investment of more than USD 500 million, according to its website.
The company sacked one person involved and placed three others on administrative leave while another resigned, it said.