Final answer:
The false statement is that detailed records of risk assessment need not be maintained.
Step-by-step explanation:
The false statement as it relates to the auditor's responsibility to document the risk assessment is b) Detailed records of risk assessment need not be maintained. When conducting a risk assessment, auditors are required to document the identification of significant risks (statement a) and the procedures performed to assess those risks (statement c). Additionally, auditors must document their responses to assessed risks (statement d) as part of their responsibility.
However, statement b is false because detailed records of risk assessment must be maintained to provide evidence of the assessment process and the auditor's decision-making.