The conflict related to a building on Oxford Tce which was bought by Silverfin Capital Ltd last year on behalf of a syndicate of investors, and leased to the CDHB.
Mr Cleverley became a director of Silverfin in May last year.
He included the company on his list of CDHB interests that month, but did not flag it as a potential conflict of interest until August, when Silverfin was in the process of buying the building.
The Ministry of Health then asked Mr Cleverley for an explanation.
It was told Mr Cleverley would stay out of any decisions around the building, but those were unlikely to happen while he was CDHB chairman.
That was because the CDHB had signed a long-term lease of the building in 2014, and the lease was not up for renegotiation until 2030.
The building was sold to Silverfin in December, but the CDHB, as tenant of the building, was not involved in the deal.
The Ministry of Health discussed the issue with the State Services Commission, and they decided the "optimal solution" would be for Mr Cleverley to resign from Silverfin.
But when that was put to Mr Cleverley, he refused to resign.
During the later investigation, Mr Cleverley told investigator Michael Heron QC: "Their view that I should resign from Silverfin was to me naively uncommercial, somewhat insulting to me (by implying I might not be trustworthy), and not justified on the facts."
Mr Heron concluded Mr Cleverley was entitled to take the position he did, but resigning from the directorship would have been "the prudent and cautious course of action here."
Mr Cleverley also part-owned an investment company with former CERA employees Gerard Gallagher and Simon Nikoloff, who the investigation found had committed "serious misconduct".
Three other former CERA employees are now being investigated for potential conflicts of interest.