"It's true that these rumors exist, but actually (the bank going bankrupt) is impossible. It's a completely different situation from the problem with the cooperatives," said Zhang Chaoyang, an official at the propaganda department of the Communist Party committee in Tinghu district, where the bank branch is located.
Zhang was referring to an incident that rattled depositors in Yancheng in January, when some rural cooperatives -- which are not subject to the supervision of the bank regulator -- ran out of cash and locked their doors.
Local officials say several co-op bosses fled after committing fraud.
China's central bank governor said this month that deposit rates are likely to liberalized in one to two years - the most explicit timeframe to date for what would be the final step in freeing up banks to set their own interest rates.
It is widely expected to introduce a deposit insurance scheme before freeing up deposit rates, to protect savers in case a liberalized market puts major strains on smaller banks and alarms the public. Analysts also expect the controls on deposit rates to be lifted gradually. Is China's debt nightmare a province called Jiangsu?
Investors both in China and globally have taken note of Beijing's recent decision to allow China's first domestic bond default. Chaori Solar Energy Science and Technology missed a bond coupon payment in March. Officials have indicated publicly that they believe other defaults are inevitable but do not believe such incidents will lead to systemic risk.
(Read more: Why China isn't ready to let trust investments fail)
In the past, domestic bond issuers were routinely bailed out by local governments and banks, and the willingness of regulators to let Chaori miss interest payments negatively impacted rates in Chinese offshore credit markets.
More recently, media also reported a heavily indebted real estate developer in Zhejiang province was at risk of defaulting on 3.5 billion yuan ($565 million) worth of loans -- a situation that has yet to be resolved.
When contacted by Reuters by phone on Tuesday, an official at the Jiangsu Sheyang Rural Commercial Bank branch hung up, saying she was busy.
An official at the administrative office at Jiangsu Sheyang Rural Commercial Bank said the bank would publish a statement shortly. On its website, the bank says it is capitalized at 525 million yuan ($85 million) and had total deposits of 12 billion yuan as of end-February,
Officials at the Jiangsu branch offices of the China Banking Regulatory Commission (CBRC) declined to comment. The Yancheng branch of CBRC and the propaganda offices in Yancheng city and Sheyang county did not answer calls seeking comment.