Hi,
a good question.
Why are you concerned about who's responsibility a fall or injury is? Does your country not offer no-fault accident health care? Or are you worried about the client suing you after the accident? Or are you worried about loosing your license?
The simple answer to your question is: It depends on whatever is written in your rehabilitation agreement/contract and consent form, which the client has signed.
And if you are negligent in your practice , then it's your fault.
Cheers,
Fyzzio