hate quoting regs but reg 3 (ii) - says Responsible person - the person who by means of their carrying on any undertaking was in control of the premise where the reportable or recordable incident happened.

So unless you hand over complete control to the contractor I read that as being the -person in charge of the site - so the company who owns it, the principle contractor if covered by CDM. For me the key word is PREMISES, it does not refer to the activity.

If it helps, my understanding is that if it is a DO under Reg7 (which includes scaffolding over 5 metres) then it is the employer's responsibility to report it i.e. the contractor. The client would of course want a copy - and this requirement can be included in the pre-construction information and the construction phase plan for a project.