After pulling its £750 million offer in May last year, Co-op bank admitted it had a £1.5 billion capital shortfall. The subsequent restructuring left it controlled by hedge funds.
Its problems were exacerbated when former bank chairman Paul Flowers was arrested during an investigation into the supply of drugs.
The Bank of England's Prudential Regulation Authority (PRA) and the Financial Conduct Authority (FCA) are conducting separate inquiries into the problems at the bank.
A planned probe by the Government will be put on hold. The FCA said this was consistent with the approaches taken during its examination of the collapses of Royal Bank of Scotland and Halifax Bank of Scotland.
The authority said it would look at the decisions and events at the bank up until June 2013, when the full extent of the bank's problems emerged.
The PRA will focus on the capital shortfall. Any failings by individuals will be scrutinised by the FCA.
Regulators have come under fire for the length of time taken to publish the findings of investigations. Previous regulator the Financial Services Authority only published its findings on RBS in late 2011.
The HBOS report has yet to be published.
After an overhaul at Co-op, the group is now run by Scot Euan Sutherland while compatriot Niall Booker heads the bank.