Its inquiry concerns Ms Rabbatts' demands that Lambeth appoints two people to the chief executive's department without any form of open competition.
In a letter sent to interim chief executive Sari Conway last week, the commission's legal director, Christopher Boothman, asked the council to delay confirming the appointments until the CRE had responded.
'If the council agrees to suspend the recruitment process pending our inquiry, it will help us to hold back from exercising our law enforcement powers. It will also protect the council's position in terms of any alleged unlawful act,' he said.
'Heather Rabbatts took legal advice on her actions relating to her appointment to Lambeth,' said a spokesperson 'She is quite confident the CRE will find everything in order.'
The extra posts Ms Rabbatts wanted to create were a personal assistant and a confidential secretary.
Tory equality spokesperson Nicholas McKay said: 'Ms Rabbatts should consider whether her position with Lambeth is now acceptable.'
The Tories were never in favour of appointing Ms Rabbatts, currently chief executive of Merton LBC, and have constantly used her unusual demands as reasons to block her appointment.
Their decision to complain to the CRE is particularly ironic, given that Ms Rabbatts is a well-known supporter of the CRE and its work.