Mr Shearsmith and a local businessman, Robert Fulton, were arrested on Monday and later bailed. The move followed complaints about a deal between the council and Mr Fulton.
Earlier in the year, the council approved a deal to acquire land in the city which is owned by Mr Fulton.
The council's solicitor and town clerk, Peter Broome, said: 'As a result of a land transaction, a complaint has been raised about the valuation of a plot of land in Durham city centre.
'The land in question has been the subject of the fullest possible public consultation over two years and has received detailed scrutiny from outside agencies such as the Valuation Office and the Audit Commission.
'I am wholly satisfied that the chief executive has acted at all times in the sole interest of the city council and the regeneration of Durham city.'
He added that Mr Shearsmith 'continues to lead the work of the city council and the development of the city centre'.