Which body cannot be held civilly or criminally liable for statements made while performing their duties?

The legislature is the correct answer because members of the legislative body have a degree of immunity when performing their official duties, especially during debates and discussions that pertain to their roles as legislators. This is rooted in the principle of legislative immunity, which is designed to protect the legislative process by ensuring that legislators can perform their functions without the fear of retaliation or legal consequences for their speech. This immunity allows them to engage freely in debate and discussion, which is essential for the functioning of a democratic government.

The other options, such as the executive branch, the judiciary, and the governor's office, do not enjoy the same level of immunity for statements made during the exercise of their duties. While there may be some protections in place for these entities, particularly regarding certain roles or actions, they do not provide the blanket protection that legislative immunity affords. Therefore, it is the legislature that is uniquely shielded from both civil and criminal liability for expressions made while conducting legislative business.