Police in Gong's native Shenmu county could not find her because she had shut off her mobile phone.
Police have asked her relatives and friends to persuade her to turn herself in or they will find and forcibly detain her, the Shaanxi provincial radio station reported on Tuesday.
The police station in Beijing, where Gong reportedly had a fake ID, declined to comment. Wang Wenjie, a publicity official from the Beijing police bureau, said he had just read the news reports and the bureau had yet to verify the allegations.
Gong told Xinhua News Agency on Friday that she forged her ID for "superstitious reasons". She also said the money used to buy properties was from her family's coal business.
The China Banking Regulatory Commission's branch in Shaanxi is reviewing Gong's financial records while she served as a deputy chief in the Shenmu bank.
The bank said it dismissed her on Saturday, and Gong claimed that she had resigned in June.
Several officials have been sacked in similar cases after they were found to hold fake IDs and hukou.
On Jan 13, the former housing administration official Zhai Zhenfeng was arrested on suspicion of corruption and expelled from the Party after a whistle-blower revealed that his family owned 31 houses in Zhengzhou, Henan province.
Zhai's daughter owned 11 properties in an affordable-housing project overseen by Zhai. Zhai and his wife, their daughter and son all had two hukou from different cities. Police have canceled the fake ones.
Former head of a tobacco monopoly bureau Chen Wenzhu was also dismissed from his post in Shanwei, Guangdong province, and expelled from the Party in October 2011, for corruption. Police found Chen had a fake ID and used it to frequently visit Hong Kong and Macao.
On Jan 16, the former police chief in Fengyang county, Anhui province, Tao Yong, stood trial on charges of bribery. He registered a fake ID in February 2011 because it was more convenient to take bribes under a false identity and conceal his fortune.
Dong Fangwei, a lawyer at Dacheng Law Offices in Beijing, said these cases have hurt the credibility of the hukou policy and weakened public trust in police.
Fake IDs and hukou can lead to serious consequences, as the holder may buy houses, rent out properties on lease, ask for bank loans, and run businesses, under a false ID, Dong said.
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